Question

HELP!!!

Mrs. Nestler enjoys listening to classical music. She has the following audio CDs by her favorite composers in her collection: 4 by Bach, 6 by Beethoven, 3 by Brahms, and 2 by Handel. If she selects 4 CDs randomly from her collection without replacing them, what is the probability that she will choose one by each composer?

A. 16/5625
B. 16/455
C. 2/5625
D. 2/455
(The answer choices, A, B, C, and D are FRACTIONS!)

Answer 1

Using the combination formula, it is found that the probability that she will choose one by each composer is given by:

144/1365.

What is the combination formula?

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by:

$C_{n,x} = \frac{n!}{x!(n-x)!}$

In this problem, she will pick 4 CDs from a set of 4 + 6 + 3 + 2 = 15, hence the total number of options is given by:

$C_{15,4} = \frac{15!}{4!11!} = 1365$

The number of options that include one from each is given by:

N = 4 x 6 x 3 x 2 = 144.

Hence the probability is given by:

p = 144/1365.

More can be learned about the combination formula at https://brainly.com/question/25821700

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