Question

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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?

Answer 1

Answer:

10.55% probability that she will choose one by each composer

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the CDs are chosen is not important. So we use the combinations formula to solve this question.

Combinations formula:

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

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

Desired outcomes:

1 Bach CD, from a set of 4.

1 Beethoven CD, from a set of 6.

1 Brahms CD, from a set of 3.

1 Handel CD, from a set of 2.

So

$D = C_{4,1}*C_{6,1}*C_{3,1}*C_{2,1} = \frac{4!}{1!(4-1)!}*\frac{6!}{1!(6-1)!}*\frac{3!}{1!(3-1)!}*\frac{2!}{1!(2-1)!} = 144$

Total outcomes:

4 CDs from a set of 4+6+3+2 = 15.

So

$T = C_{15,4} = \frac{15!}{4!(15-4)!} = 1365$

Probability:

$p = \frac{D}{T} = \frac{144}{1365} = 0.1055$

10.55% probability that she will choose one by each composer