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Find the number of ways to listen to four CDs from a selection of 8 CDs.? A. 1680 B. 336 C. 70 D. 50

1 Answer

May 11, 2018

$^{8} P_{4} = 1680$ $""^8P_4 = 1680$ , i.e. choice A.

Explanation:

Note that the order of the CDs does matter, so we are wanting $^{8} P_{4}$ $""^8P_4$ rather than $^{8} C_{4}$ $""^8C_4$ ...

$^{8} P_{4} = \frac{8!}{(8 - 4)!} = 8 \cdot 7 \cdot 6 \cdot 5 = 1680$ $""^8P_4 = (8!)/((8-4)!) = 8*7*6*5 = 1680$

In other words, there are $8$ $8$ choices for the first CD, $7$ $7$ for the second, $6$ $6$ for the third and $5$ $5$ for the fourth.

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