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A certain football coach allows his quarterback to call thre

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anceer
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A certain football coach allows his quarterback to call thre [#permalink] New post   12 Jul 2014, 23:52
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A certain football coach allows his quarterback to call three plays in a row. If the quarterback can choose from 3 passing plays, 4 running plays, and 2 trick plays, how many different arrangements of plays can be run, if the same play can’t be run more than once?

A. 24
B. 125
C. 243
D. 504
E. 729
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bankerboy30
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Re: A certain football coach allows his quarterback to call thre [#permalink] New post   13 Jul 2014, 07:21
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Bunuel : is this approach correct.

Number of ways to choose the first play: 9
Second play: 8
Third:7

9*8*7= 504
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Re: A certain football coach allows his quarterback to call thre [#permalink] New post   13 Jul 2014, 05:18
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anceer wrote:
A certain football coach allows his quarterback to call three plays in a row. If the quarterback can choose from 3 passing plays, 4 running plays, and 2 trick plays, how many different arrangements of plays can be run, if the same play can’t be run more than once?

A. 24
B. 125
C. 243
D. 504
E. 729


P=3, R=4, and T=2.

There are following cases possible:

1. Different kinf of plays:

PRT (Any combination) = 3*4*2*3!=144.

2. Two same kind of plays and one from other kind of play:

PPR (Any combination. Notice that the two P's here must be different) = \(C^2_3*4*3!=72\);
PPT = \(C^2_3*2*3!=36\);

RRP = \(C^2_4*3*3!=108\);
RRT = \(C^2_4*2*3!=72\);

TTP = \(C^2_2*3*3!=18\);
TTR = \(C^2_2*4*3!=24\);

3. All three plays are of the same kind:

PPP = C^3_3*3!=6
RRR = C^3_4*3!=24
TTT is not possible because we have only two T's.

Total = 144 + 72 + 36 + 108 + 72 + 18 + 24 + 6 + 24 = 504.

Answer: D.
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Re: A certain football coach allows his quarterback to call thre [#permalink] New post   23 Jul 2014, 08:52
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But the question said 'same play can’t be run more than once'. So I got 144 as my answer. Am I missing something. Please help!!!
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Re: A certain football coach allows his quarterback to call thre [#permalink] New post   13 Jul 2014, 09:28
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bankerboy30 wrote:
Bunuel : is this approach correct.

Number of ways to choose the first play: 9
Second play: 8
Third:7

9*8*7= 504


Yes. That's correct.
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A certain football coach allows his quarterback to call thre [#permalink] New post   04 Jun 2023, 04:29
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Number of ways to choose 3 out of 9 = 9C3 = 84
Number of ways to arrange 3 items = 3 ! = 6
So total number of ways of arranging the plays after choosing = 84 * 6 =504

Option D
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Re: A certain football coach allows his quarterback to call thre [#permalink] New post   23 Jul 2014, 10:57
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vivekisthere wrote:
But the question said 'same play can’t be run more than once'. So I got 144 as my answer. Am I missing something. Please help!!!


Yes, the same play can’t be run more than once but the kinds of plays could repeat. For example, PPT is valid because P's there are two different passing plays out of 3.
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Re: A certain football coach allows his quarterback to call thre [#permalink] New post   23 Apr 2018, 02:42
anceer wrote:
A certain football coach allows his quarterback to call three plays in a row. If the quarterback can choose from 3 passing plays, 4 running plays, and 2 trick plays, how many different arrangements of plays can be run, if the same play can’t be run more than once?

A. 24
B. 125
C. 243
D. 504
E. 729


The question has played smartly with the words where it says "Same play can't be run more than once" and not "Same category of play can't be run more than once"..

After understanding this, question becomes really simple as categorization of play as passing play, running play and trick play doesn't have any role in selecting the three plays and the total arrangements will be 9*8*7 = 504..

Though i don't understand such kind of wordings in a quant question of GMAT as QA question is framed to test quantitative skill and not VA skill..
Really a tricky question if one doesn't pay heed to wordings..
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Re: A certain football coach allows his quarterback to call thre [#permalink] New post   21 Feb 2022, 10:07
The quarterback can call three plays in a row. All different.

Each move can be chosen from any of the following types:

3 passing plays
4 running plays
2 trick plays

Total of the types of plays = 9

E1 E2 E3, the quarterback has three spaces to fill with any of the 9 plays, and cannot replay.

then

E1=9
E2 = 8 (of the 9, he already occupied a move in E1)
E3 = 7

Then

9x8x7 = ...4, number result where the unit figure is 4, we see the alternatives that have unit 4.

A) 24 It is not, by simple inspection (multiplication of three numbers greater than equal to 7).
D) 504 is the correct alternative.

Answer D
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Re: A certain football coach allows his quarterback to call thre [#permalink]
21 Feb 2022, 10:07
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