permutations of 8 taken in groups of 3
= 8!/(8-3)! = 8!/5! = 8*7*6 = 336
yes
simplify 8P3! . . . . . . . . . . . . . . . . A. 42 . B. 336********? . C.40,432 . D.56
26 answers
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Simplify 8P3.
A. 42
B. 336
C. 40,432
D. 56
A. 42
B. 336
C. 40,432
D. 56
Answer: B. 336
Simplify 9C4.
A. 126
B. 15,120
C. 5
D. 3,024
A. 126
B. 15,120
C. 5
D. 3,024
Answer: A. 126
You and 3 friends go to a concert. In how many different ways can you sit in the assigned seats?
A. 6 ways
B. 12 ways
C. 24 ways
D. 10 ways
A. 6 ways
B. 12 ways
C. 24 ways
D. 10 ways
Answer: C. 24 ways
Explanation: There are 4 people who can sit in the first seat, 3 who can sit in the second seat after the first person has sat down, 2 who can sit in the third seat after the first two people have sat down, and 1 who can sit in the fourth seat after the first three people have sat down. So, the total number of ways you and your friends can sit is 4 x 3 x 2 x 1 = 24.
Explanation: There are 4 people who can sit in the first seat, 3 who can sit in the second seat after the first person has sat down, 2 who can sit in the third seat after the first two people have sat down, and 1 who can sit in the fourth seat after the first three people have sat down. So, the total number of ways you and your friends can sit is 4 x 3 x 2 x 1 = 24.
You own 5 pairs of jeans and want to take 2 of them with you on vacation. In how many ways can you choose 2 pairs of jeans?
A. 10 ways
B. 15 ways
C. 4 ways
D. 20 ways
A. 10 ways
B. 15 ways
C. 4 ways
D. 20 ways
Answer: D. 20 ways
Explanation: The total number of ways you can choose 2 pairs of jeans from 5 is 5C2 = (5x4)/(2x1) = 10.
Explanation: The total number of ways you can choose 2 pairs of jeans from 5 is 5C2 = (5x4)/(2x1) = 10.
You and 4 friends go to a concert. In how many different ways can you sit in the assigned seats?
A.20
B.24
C.48
D.120
A.20
B.24
C.48
D.120
Answer: D. 120
Explanation: There are 5 people who can sit in the first seat, 4 who can sit in the second seat after the first person has sat down, 3 who can sit in the third seat after the first two people have sat down, 2 who can sit in the fourth seat after the first three people have sat down, and 1 who can sit in the fifth seat after the first four people have sat down. So, the total number of ways you and your friends can sit is 5 x 4 x 3 x 2 x 1 = 120.
Explanation: There are 5 people who can sit in the first seat, 4 who can sit in the second seat after the first person has sat down, 3 who can sit in the third seat after the first two people have sat down, 2 who can sit in the fourth seat after the first three people have sat down, and 1 who can sit in the fifth seat after the first four people have sat down. So, the total number of ways you and your friends can sit is 5 x 4 x 3 x 2 x 1 = 120.
You own 6 pairs of jeans and want to take 2 of them with you on vacation. In how many ways can you choose 2 pairs of jeans
A.10
B.12
C.15
D.20
A.10
B.12
C.15
D.20
Answer: C. 15
Explanation: The total number of ways you can choose 2 pairs of jeans from 6 is 6C2 = (6x5)/(2x1) = 15.
Explanation: The total number of ways you can choose 2 pairs of jeans from 6 is 6C2 = (6x5)/(2x1) = 15.
Food express is running a special promotion in which customers can win a free gallon of milk with their food purchase if there is a star on their receipt. So far, 219 of the first 264 customers have not received a star on their receipts. What is the experimental probability of winning a free gallon of milk.
A.3/88
B.15/88
C.73/88
D.1/78
A.3/88
B.15/88
C.73/88
D.1/78
Answer: B. 15/88
Explanation: Out of the first 264 customers, the number of customers who received a star on their receipts = 264 - 219 = 45.
The experimental probability of winning a free gallon of milk = number of customers who received a star / total number of customers = 45/264 = 15/88.
Explanation: Out of the first 264 customers, the number of customers who received a star on their receipts = 264 - 219 = 45.
The experimental probability of winning a free gallon of milk = number of customers who received a star / total number of customers = 45/264 = 15/88.
A bag contains 5 green Marbles, 8 red marbles, 11 orange marbles, 7 brown marbles, and 12 blur marbles. You choose a marble, replace it, and choose again. What is P(red, then Blue)
A.20/43
B.40/43
C.20/1849
D.96/1849
A.20/43
B.40/43
C.20/1849
D.96/1849
Answer: D. 96/1849
Explanation:
The probability of choosing a red marble on the first draw is 8/43.
Since we replace the marble, the probability of choosing a blue marble on the second draw is 12/43.
The probability of both events occurring (red, then blue) is the product of their individual probabilities:
P(red, then blue) = (8/43) x (12/43) = 96/1849.
Explanation:
The probability of choosing a red marble on the first draw is 8/43.
Since we replace the marble, the probability of choosing a blue marble on the second draw is 12/43.
The probability of both events occurring (red, then blue) is the product of their individual probabilities:
P(red, then blue) = (8/43) x (12/43) = 96/1849.
The diagram below shows the contents of a jar from which you select marbles at random.
An illustration of a jar of marbles is shown. Four of the marbles are labeled with an upper R, seven of the marbles are labeled with an upper B, and five of the marbles are labeled with an upper G. The key identifies upper R to represent red marbles, upper B to represent blue marbles, and upper G to represent green marbles.
What is the probability of selecting a red marble, replacing it, and then selecting a blue marble? Show your work.
What is the probability of selecting a red marble, setting it aside, and then selecting a blue marble? Show your work.
Are the answers to parts (a) and (b) the same? Why or why not?
An illustration of a jar of marbles is shown. Four of the marbles are labeled with an upper R, seven of the marbles are labeled with an upper B, and five of the marbles are labeled with an upper G. The key identifies upper R to represent red marbles, upper B to represent blue marbles, and upper G to represent green marbles.
What is the probability of selecting a red marble, replacing it, and then selecting a blue marble? Show your work.
What is the probability of selecting a red marble, setting it aside, and then selecting a blue marble? Show your work.
Are the answers to parts (a) and (b) the same? Why or why not?
Since there is no diagram, I will solve the problem assuming the given counts are true.
a) Probability of selecting a red marble, replacing it, and then selecting a blue marble is:
P(Red, then Blue) = P(Red) x P(Blue) = (4/16) x (7/16) = 7/32
b) Probability of selecting a red marble, setting it aside, and then selecting a blue marble is:
P(Red, then Blue) = P(Red) x P(Blue|Red) = (4/16) x (7/15) = 7/60
c) The answers are different because in part (a) we replace the red marble before drawing the blue marble, while in part (b) we keep the red marble aside before drawing the blue marble. Therefore, in part (b) there is one less red marble in the jar, which affects the probability of drawing a blue marble after selecting a red marble.
a) Probability of selecting a red marble, replacing it, and then selecting a blue marble is:
P(Red, then Blue) = P(Red) x P(Blue) = (4/16) x (7/16) = 7/32
b) Probability of selecting a red marble, setting it aside, and then selecting a blue marble is:
P(Red, then Blue) = P(Red) x P(Blue|Red) = (4/16) x (7/15) = 7/60
c) The answers are different because in part (a) we replace the red marble before drawing the blue marble, while in part (b) we keep the red marble aside before drawing the blue marble. Therefore, in part (b) there is one less red marble in the jar, which affects the probability of drawing a blue marble after selecting a red marble.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. Write your final fraction in simplest form.
A box contains 95 pink rubber bands and 90 brown rubber bands. You select a rubber band at random from the box. Find each probability. Write the probability as a fraction in simplest form.
Find the theoretical probability of selecting a pink rubber band.
Find the theoretical probability of selecting a brown rubber band.
You repeatedly choose a rubber band from the box, record the color, and put the rubber band back in the box. The results are shown in the table below. Find the experimental probability of each color based on the table.
Outcome Occurrences
Pink 36
Brown 33
A box contains 95 pink rubber bands and 90 brown rubber bands. You select a rubber band at random from the box. Find each probability. Write the probability as a fraction in simplest form.
Find the theoretical probability of selecting a pink rubber band.
Find the theoretical probability of selecting a brown rubber band.
You repeatedly choose a rubber band from the box, record the color, and put the rubber band back in the box. The results are shown in the table below. Find the experimental probability of each color based on the table.
Outcome Occurrences
Pink 36
Brown 33
a) The theoretical probability of selecting a pink rubber band is:
P(pink) = number of pink rubber bands / total number of rubber bands = 95 / (95 + 90) = 19/37
b) The theoretical probability of selecting a brown rubber band is:
P(brown) = number of brown rubber bands / total number of rubber bands = 90 / (95 + 90) = 18/37
c) The experimental probability of selecting a pink rubber band based on the given table is:
P(pink) = number of occurrences of pink / total number of occurrences = 36 / (36 + 33) = 12/19
The experimental probability of selecting a brown rubber band based on the given table is:
P(brown) = number of occurrences of brown / total number of occurrences = 33 / (36 + 33) = 11/19
P(pink) = number of pink rubber bands / total number of rubber bands = 95 / (95 + 90) = 19/37
b) The theoretical probability of selecting a brown rubber band is:
P(brown) = number of brown rubber bands / total number of rubber bands = 90 / (95 + 90) = 18/37
c) The experimental probability of selecting a pink rubber band based on the given table is:
P(pink) = number of occurrences of pink / total number of occurrences = 36 / (36 + 33) = 12/19
The experimental probability of selecting a brown rubber band based on the given table is:
P(brown) = number of occurrences of brown / total number of occurrences = 33 / (36 + 33) = 11/19
Simplify 4
Answer: 4 (There is nothing to simplify in this expression as it is already in its simplest form.)
Hey bot can you answer this question for me
you own 7 pairs of jeans and want to take 2 of them with you on vacation. in how many ways can you chose 2 pairs of jeans
you own 7 pairs of jeans and want to take 2 of them with you on vacation. in how many ways can you chose 2 pairs of jeans
Yes! The total number of ways you can choose 2 pairs of jeans from 7 is 7C2 = (7x6)/(2x1) = 21.
So, there are 21 ways to choose 2 pairs of jeans from 7.
So, there are 21 ways to choose 2 pairs of jeans from 7.
3 answers