A bag contains tiles with the letters A-R-I-T-H-M-E-T-I-C. Amelia chooses a tile without looking and doesn’t replace it. She chooses a second tile without looking. What is the probability that she will choose the letter I both times?
A. start fraction 1 over 25 end fraction
B. Start Fraction 1 over 45 End Fraction
C. start fraction 2 over 45 end fraction
D. start fraction 2 over 55 end fraction
5 answers
There are a total of 11 tiles with the letter I out of 12 tiles in total. After Amelia chooses one tile without replacement, there are only 10 tiles left and only 1 with the letter I. The probability of choosing the letter I on the second pick is therefore 1/10. The probability of choosing the letter I both times is the product of those probabilities: 11/12 x 1/10 = 11/120. This reduces to Start Fraction 11 over 120 End Fraction, which is answer choice D.
A sandwich shop offers the following toppings. How many two-topping sandwiches can you make?
lettuce
tomato
bacon
cheese
mustard
A. 8
B. 10
C. 12
D. 20
lettuce
tomato
bacon
cheese
mustard
A. 8
B. 10
C. 12
D. 20
To count the number of two-topping sandwiches, we need to use the combination formula:
n choose k = n! / (k!*(n-k)!)
where n is the total number of items and k is the number of items we want to choose.
In this case, we have 5 toppings and we want to choose 2, so:
5 choose 2 = 5! / (2!*(5-2)!) = 10
Therefore, there are 10 two-topping sandwiches that can be made. The answer is B.
n choose k = n! / (k!*(n-k)!)
where n is the total number of items and k is the number of items we want to choose.
In this case, we have 5 toppings and we want to choose 2, so:
5 choose 2 = 5! / (2!*(5-2)!) = 10
Therefore, there are 10 two-topping sandwiches that can be made. The answer is B.
Alli's ice cream shop offers 5 flavors and 10 toppings. Jali's ice cream shop offers 7 flavors and 7 toppings. Fernando's ice cream shop offers 9 flavors and 6 toppings. Laura's ice cream shop offers 13 flavors and 4 toppings.
If you want one flavor of ice cream and one topping, which shop gives you the most options?
A. Alli's ice cream shop
B. Jali's ice cream shop
C. Fernando's ice cream shop
D. Laura's ice cream shop
If you want one flavor of ice cream and one topping, which shop gives you the most options?
A. Alli's ice cream shop
B. Jali's ice cream shop
C. Fernando's ice cream shop
D. Laura's ice cream shop
To calculate the number of options for one flavor of ice cream and one topping, we need to multiply the number of flavors by the number of toppings for each shop, and then compare the results.
For Alli's ice cream shop: 5 x 10 = 50 options
For Jali's ice cream shop: 7 x 7 = 49 options
For Fernando's ice cream shop: 9 x 6 = 54 options
For Laura's ice cream shop: 13 x 4 = 52 options
Therefore, the ice cream shop with the most options for one flavor of ice cream and one topping is Fernando's, with 54 options. The answer is C.
For Alli's ice cream shop: 5 x 10 = 50 options
For Jali's ice cream shop: 7 x 7 = 49 options
For Fernando's ice cream shop: 9 x 6 = 54 options
For Laura's ice cream shop: 13 x 4 = 52 options
Therefore, the ice cream shop with the most options for one flavor of ice cream and one topping is Fernando's, with 54 options. The answer is C.