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# At a high school assembly, the principal plans to give out

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Manager
Status: Current MBA Student
Joined: 19 Nov 2009
Posts: 89
Concentration: Finance, General Management
GMAT 1: 720 Q49 V40
At a high school assembly, the principal plans to give out  [#permalink]

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17 Jul 2010, 15:50
1
00:00

Difficulty:

55% (hard)

Question Stats:

53% (02:30) correct 47% (01:40) wrong based on 28 sessions

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Question #10 (incorrect)

Hello Forum,

I wanted your take as to the most efficient course of action regarding solving a problem such as the one below. I would appreciate it if you could walk me through your work and thought process. I'm having trouble with these question types. Thanks!

At a high school assembly, the principal plans to give out awards for extraordinary achievement. The nominees for the awards are the most highly rated teachers and the students with the most improved GPAs. How many different groups of award recipients can be chosen in which at least one recipient is a teacher? (Two groups of award recipients are considered different if at least one group member is different.)

(A) 20
(B) 30
(C) 46
(D) 60
(E) 120
Math Expert
Joined: 02 Sep 2009
Posts: 64240
Re: Combo Problem from Knewton CAT  [#permalink]

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17 Jul 2010, 16:04
1
Pleas check th questions before posting. Original question is below:

At a high school assembly, the principal plans to give out 3 awards for extraordinary achievement. The nominees for the awards are the 3 most highly rated teachers and the 5 students with the most improved GPAs. How many different groups of award recipients can be chosen in which at least one recipient is a teacher? (Two groups of award recipients are considered different if at least one group member is different.)

(A) 20
(B) 30
(C) 46
(D) 60
(E) 120

There are total of 3+5=8 nominees.

# of different groups of 3 out of 8 nominees with AT LEAST 1 teacher = total # of different groups of 3 out of 8 nominees minus # of different groups of 3 with ONLY students (with no teacher in them) --> $$C^3_8-C^3_5=46$$.

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Posts: 15015
Re: At a high school assembly, the principal plans to give out  [#permalink]

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26 Nov 2016, 03:35
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Re: At a high school assembly, the principal plans to give out   [#permalink] 26 Nov 2016, 03:35