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Cade
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Homework Statement
A particular iPod playlist contains 100 songs, 10 of which are by the Beatles. What is the probability that the
first Beatles song heard is the fifth song played?
Homework Equations
Combinatorics: permutation, combinations.
The Attempt at a Solution
The number of desired outcomes for the event is:
90*89*88*87 (choose 4 of 90 songs that aren't Beatles)
* 10 (choose 1 song that is Beatles)
The sample space is:
100*99*98*97*96 (choose 5 of 100 songs from the playlist)
The correct answer is (90*89*88*87*10)/(100*99*98*97*96).
How would I solve this problem using the formulae for combinations? I tried it this way, but the answer was incorrect: C(90,4)*C(10,1)/C(100,5)
As I understand it, the order within the non-Beatles set is irrelevant, but using P(90,4)P(10,1)/P(100,5) works. What am I missing?