Question

I have a jar of red and green M&M's with 55% red M&M's. I plan to pick 7. How many different ways can you get 2 red M&M's out of 7? Use the formula for the binomial coefficient to find that number.

A) 35
B) 21
C) 15
D) 10

Answer 1

Using the binomial coefficient formula, there are 21 different ways to get exactly 2 red M&M's out of 7, corresponding to answer choice B.

Step-by-step explanation:

To find the number of different ways to get 2 red M&M's out of 7 when picking from the jar, we use the binomial coefficient. The general formula for a binomial coefficient is given by C(n, k) = n! / (k!(n-k)!), where n is the total number of items, k is the number of items to choose, n! is the factorial of n, and k! is the factorial of k.

In this case, n is 7 (since we are picking 7 M&M's), and k is 2 (because we are looking for the ways to get exactly 2 red M&M's). Thus, we calculate C(7, 2) which is 7! / (2!(7-2)!) = 7! / (2!5!) = (7x6) / (2x1) = 42 / 2 = 21.

Therefore, the number of different ways you can get exactly 2 red M&M's out of 7 is 21, which corresponds to answer choice B.