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In how many ways can a sample of 4 CD players be selected from 35 CD players for inspection? Assume that no CD player will be selected for testing more than once.

A) 6,041,796 ways
B) 8,356,750 ways
C) 9,129,575 ways
D) 11,451,000 ways

1 Answer

4 votes

Final answer:

A sample of 4 CD players can be selected from 35 CD players in 52,360 different ways, using combinations. None of the options provided matches this calculation.

Step-by-step explanation:

To determine in how many ways a sample of 4 CD players can be selected from 35 CD players for inspection, where no CD player is selected more than once, we use combinations. In mathematics, combinations are used to find out how many different ways you can choose 'r' items from 'n' items, where the order does not matter and without repetitions. This is mathematically represented as C(n, r) or sometimes as 'n choose r' and can be calculated using the formula: C(n, r) = n! / [r! (n - r)!]. In this case, we are choosing 4 CD players for inspection from a group of 35, so 'n' is 35 and 'r' is 4. Plugging these values into the formula, we get C(35, 4) = 35! / [4! (35 - 4)!] = (35*34*33*32) / (4*3*2*1) = 52,360. Therefore, from the options provided, none of them match our calculation; hence, perhaps there was an error in the question or answer choices given.

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