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# An equal number of juniors and seniors are trying out for six spots

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Senior Manager
Joined: 24 Jun 2012
Posts: 378
Location: Pakistan
GPA: 3.76
An equal number of juniors and seniors are trying out for six spots  [#permalink]

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19 Jul 2017, 05:00
1
00:00

Difficulty:

65% (hard)

Question Stats:

61% (02:03) correct 39% (02:28) wrong based on 81 sessions

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An equal number of juniors and seniors are trying out for six spots on the university debating team. If the team must consist of at least four seniors, then how many different possible debating teams can result if five juniors try out?

A) 50
(B) 55
(C) 75
(D) 100
(E) 250

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An equal number of juniors and seniors are trying out for six spots  [#permalink]

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19 Jul 2017, 05:14
sananoor wrote:
An equal number of juniors and seniors are trying out for six spots on the university debating team. If the team must consist of at least four seniors, then how many different possible debating teams can result if five juniors try out?

A) 50
(B) 55
(C) 75
(D) 100
(E) 250

Five juniors and five seniors (an equal number of juniors and seniors) should form 6-member team so that the team consists of at least four seniors (4, or 5 seniors, all 6 cannot be seniors since there are only 5 seniors).

1. 4 seniors and 2 juniors: $$C^4_5*C^2_5=5*10=50$$

2. 5 seniors and 1 juniors: $$C^5_5*C^1_5=1*5=5$$

Total = 50 + 5 = 55.

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Re: An equal number of juniors and seniors are trying out for six spots  [#permalink]

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14 Sep 2018, 11:54
@
Bunuel wrote:
sananoor wrote:
An equal number of juniors and seniors are trying out for six spots on the university debating team. If the team must consist of at least four seniors, then how many different possible debating teams can result if five juniors try out?

A) 50
(B) 55
(C) 75
(D) 100
(E) 250

Five juniors and five seniors (an equal number of juniors and seniors) should form 6-member team so that the team consists of at least four seniors (4, or 5 seniors, all 6 cannot be seniors since there are only 5 seniors).

1. 4 seniors and 2 juniors: $$C^4_5*C^2_5=5*10=50$$

2. 5 seniors and 1 juniors: $$C^5_5*C^1_5=1*5=5$$

Total = 50 + 5 = 55.

Here is a Doubt.

Why not 6 Seniors and 0 Juniors?

Aren't we missing 1 more case 6C6x5C0 = 1?

I am new to the GMAT Club, So I Don't know How to tag @Banuel
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Joined: 05 Jun 2018
Posts: 24
Location: United States (TN)
GMAT 1: 730 Q47 V44
GPA: 3
Re: An equal number of juniors and seniors are trying out for six spots  [#permalink]

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14 Sep 2018, 12:12
1
rajk3433 wrote:
@
Bunuel wrote:
sananoor wrote:
An equal number of juniors and seniors are trying out for six spots on the university debating team. If the team must consist of at least four seniors, then how many different possible debating teams can result if five juniors try out?

A) 50
(B) 55
(C) 75
(D) 100
(E) 250

Five juniors and five seniors (an equal number of juniors and seniors) should form 6-member team so that the team consists of at least four seniors (4, or 5 seniors, all 6 cannot be seniors since there are only 5 seniors).

1. 4 seniors and 2 juniors: $$C^4_5*C^2_5=5*10=50$$

2. 5 seniors and 1 juniors: $$C^5_5*C^1_5=1*5=5$$

Total = 50 + 5 = 55.

Here is a Doubt.

Why not 6 Seniors and 0 Juniors?

Aren't we missing 1 more case 6C6x5C0 = 1?

I am new to the GMAT Club, So I Don't know How to tag @Banuel

Hi,

We have an equal number of juniors and seniors. The problem states that we have 5 juniors, thus we only have 5 seniors. To make a team of 6 using a selection of 5 juniors and 5 seniors, the team must consist of at least 1 junior.

Does this make sense? To make a team of 6 seniors, you would need at least one more senior - the problem states that we only have 5.

I hope this helps -
Re: An equal number of juniors and seniors are trying out for six spots   [#permalink] 14 Sep 2018, 12:12
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