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Counting problem from Veritas

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by Mo2men » Tue Mar 21, 2017 3:48 pm
Mike, a DJ at a high school radio station, needs to play two or three more songs before the end of the school dance. If each composition must be selected from a list of the 10 most popular songs of the year, how many unique song schedules are available for the remainder of the dance, if the songs cannot be repeated?
(A) 6
(B) 90
(C) 120
(D) 720
(E) 810

OA: E

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by Brent@GMATPrepNow » Tue Mar 21, 2017 4:54 pm
Mo2men wrote:Mike, a DJ at a high school radio station, needs to play two or three more songs before the end of the school dance. If each composition must be selected from a list of the 10 most popular songs of the year, how many unique song schedules are available for the remainder of the dance, if the songs cannot be repeated?
(A) 6
(B) 90
(C) 120
(D) 720
(E) 810
2-song arrangements
There are 10 ways to select a 1st song
There are 9 ways to select a 2nd song
So, the total number of 2-song arrangements = (10)(9) = 90

3-song arrangements
There are 10 ways to select a 1st song
There are 9 ways to select a 2nd song
There are 8 ways to select a 3rd song
So, the total number of 3-song arrangements = (10)(9)(8) = 720

TOTAL number of schedules = 90 + 720 = 810

Answer: E

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Brent
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