counting principle hard example with no answer
11 answers
A group of friends is planning a road trip to five different cities. They have a list of 10 possible cities they would like to visit, but they can only choose 5 for this trip. In how many different ways can they choose the cities they will visit on their road trip?
different question
A school is offering 7 different elective courses and each student must choose 3 elective courses to take for the semester. In how many different ways can a student choose their elective courses?
what is the answer
There are multiple ways to calculate the answer to this question, depending on whether the order of the courses chosen matters. If the order does not matter and we are selecting 3 courses from 7, we can use the combination formula:
C(n, r) = n! / (r!(n-r)!)
where n is the total number of courses (7) and r is the number of courses to be chosen (3).
Plugging in the values, we get:
C(7, 3) = 7! / (3!(7-3)!) = 7! / (3!4!) = 35
Therefore, there are 35 different ways for a student to choose their elective courses if the order does not matter.
C(n, r) = n! / (r!(n-r)!)
where n is the total number of courses (7) and r is the number of courses to be chosen (3).
Plugging in the values, we get:
C(7, 3) = 7! / (3!(7-3)!) = 7! / (3!4!) = 35
Therefore, there are 35 different ways for a student to choose their elective courses if the order does not matter.
do a 7th grade problem now
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A box contains 4 red marbles, 3 blue marbles, and 2 green marbles. If a marble is selected at random from the box, what is the probability that it is either red or blue?
A box contains 4 red marbles, 3 blue marbles, and 2 green marbles. If a marble is selected at random from the box, what is the probability that it is either red or blue?
counting princible easy 7th grade question with answer
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A school is offering 4 different language classes and 3 different art classes. In how many ways can a student choose one language class and one art class to take for the semester?
Answer: The student can choose one language class in 4 ways and one art class in 3 ways. Using the counting principle, the total number of ways the student can choose one language class and one art class is 4 x 3 = 12 ways.
A school is offering 4 different language classes and 3 different art classes. In how many ways can a student choose one language class and one art class to take for the semester?
Answer: The student can choose one language class in 4 ways and one art class in 3 ways. Using the counting principle, the total number of ways the student can choose one language class and one art class is 4 x 3 = 12 ways.
add a 3rd variable
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A school is offering 4 different language classes, 3 different art classes, and 2 different music classes. In how many ways can a student choose one language class, one art class, and one music class to take for the semester?
Answer: The student can choose one language class in 4 ways, one art class in 3 ways, and one music class in 2 ways. Using the counting principle, the total number of ways the student can choose one language class, one art class, and one music class is 4 x 3 x 2 = 24 ways.
A school is offering 4 different language classes, 3 different art classes, and 2 different music classes. In how many ways can a student choose one language class, one art class, and one music class to take for the semester?
Answer: The student can choose one language class in 4 ways, one art class in 3 ways, and one music class in 2 ways. Using the counting principle, the total number of ways the student can choose one language class, one art class, and one music class is 4 x 3 x 2 = 24 ways.