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vikasp99
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Mike, a DJ at a high school radio station, needs to play two or three 24 Feb 2017, 10:13
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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45% (medium)

Question Stats:

62% (01:31) correct 38% (01:53) wrong based on 673 sessions

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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
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E
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mikemcgarry
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Mike, a DJ at a high school radio station, needs to play two or three 24 Feb 2017, 17:16
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vikasp99
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
Show more
Dear vikasp99,

I'm happy to respond. :-) This is another good Veritas question.

For this question, we will use the Fundamental Counting Principle.

We can have either two-song lists or three-song lists. We will count them separate an add. Notice that having the same songs in different orders count as different playlists, according to this setup.

For two-song lists, DJ Mike has 10 choices for the first song, and then 9 remaining choices for the second song. This means
# of two-song playlists = 10*9 = 90

For three-song lists, DJ Mike has 10 choices for the first song, then 9 remaining choices for the second song, then 8 remaining choices for the third song. This means
# of three-song playlists = 10*9*8 = 10*72 = 720

Add those
total number of playlists = 720 + 90 = 810
OA = (E)

That's a great problem!

Does all this make sense?
Mike :-)
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Mike, a DJ at a high school radio station, needs to play two or three 19 Mar 2017, 22:12
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mikemcgarry
vikasp99
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
Dear vikasp99,

I'm happy to respond. :-) This is another good Veritas question.

For this question, we will use the Fundamental Counting Principle.

We can have either two-song lists or three-song lists. We will count them separate an add. Notice that having the same songs in different orders count as different playlists, according to this setup.

For two-song lists, DJ Mike has 10 choices for the first song, and then 9 remaining choices for the second song. This means
# of two-song playlists = 10*9 = 90

For three-song lists, DJ Mike has 10 choices for the first song, then 9 remaining choices for the second song, then 8 remaining choices for the third song. This means
# of three-song playlists = 10*9*8 = 10*72 = 720

Add those
total number of playlists = 720 + 90 = 810
OA = (E)

That's a great problem!

Does all this make sense?
Mike :-)
Show more


Hi mikemcgarry,

Are we using permutations and not combinations because it says unique sequences and thus order matters ?
I'm new to combinatorics and so, my concepts are extremely shaky when it comes to identifying when does the arrangement matter and when does it not. Kindly help.

Thanks in advance.
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Mike, a DJ at a high school radio station, needs to play two or three 20 Mar 2017, 00:50
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vikasp99
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
Show more

if he plays 2 songs , no. of ways it can be scheduled = 10C2 x 2! = 90

if he plays 3 songs , no. of ways it can be scheduled = 10C3 x 3! = 720

therefore total ways = 720 +90 =810

Option E
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Mike, a DJ at a high school radio station, needs to play two or three 20 Mar 2017, 11:47
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Shruti0805
Hi mikemcgarry,

Are we using permutations and not combinations because it says unique sequences and thus order matters ?
I'm new to combinatorics and so, my concepts are extremely shaky when it comes to identifying when does the arrangement matter and when does it not. Kindly help.

Thanks in advance.
Show more
Dear Shruti0805,

I'm happy to respond. :-)

Yes, this question's prompt could have been slightly more explicit about this. The GMAT is often very explicit. Nevertheless, the phrase "unique song schedules" implies that having the same songs in a different order implies a different schedule.

Also, I would say, think about the real world. The very best thing you can do on the real GMAT is to think about the real world as a touchstone. Suppose we have two (imaginary) songs for our playlist. (I just made up both of these titles, but for all I know, someone has written one of these songs!)

Song Schedule #1:
1) "Now My Heart is Broken"
2) "I'm Ready for Love Again"
That's an optimistic and hopeful way for the dance to end.

Song Schedule #2:
1) "I'm Ready for Love Again"
2) "Now My Heart is Broken"
Ouch! In that order, the message is considerably less appealing! Everyone would leave the dance depressed!

Does all this make sense?
Mike :-)
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Mike, a DJ at a high school radio station, needs to play two or three 13 Sep 2021, 10:48
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KrishnakumarKA1
vikasp99
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

if he plays 2 songs , no. of ways it can be scheduled = 10C2 x 2! = 90

if he plays 3 songs , no. of ways it can be scheduled = 10C3 x 3! = 720

therefore total ways = 720 +90 =810

Option E
Show more

-----------------------
Why are we "x 2!" or "x 3!" when we are anyways doing 10C2 & 10C3?
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Mike, a DJ at a high school radio station, needs to play two or three 13 Sep 2021, 13:08
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If he plays 2 songs:
10*9=90 combinations
If he plays 3 songs:
10*9*8=720 combinations
90+720=810 combinations total
Ans=E
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RastogiSarthak99
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Mike, a DJ at a high school radio station, needs to play two or three 27 Nov 2023, 12:03
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I went with simply 10P2 + 10P3 which is equivalent to 810
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Mike, a DJ at a high school radio station, needs to play two or three 17 Feb 2025, 07:59
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