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# In how many ways can a coach select a university team from a pool of

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Math Expert
Joined: 02 Sep 2009
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In how many ways can a coach select a university team from a pool of [#permalink]

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06 Mar 2018, 07:18
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25% (medium)

Question Stats:

80% (00:39) correct 20% (01:48) wrong based on 54 sessions

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In how many ways can a coach select a university team from a pool of eligible candidates?

(1) The number of eligible candidates is three times greater than the number of slots on the team.
(2) 60% of the 20 athletes are eligible to play on the four-person university team.
[Reveal] Spoiler: OA

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In how many ways can a coach select a university team from a pool of [#permalink]

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06 Mar 2018, 09:29
From 1
The number of eligible candidates is three times greater than the number of slots on the team.
let slots be n
Let the number of eligible candidates be x then x=3n
then also we can not calculate no of ways

From 2
60% of the 20 athletes are eligible to play on the four-person university team.

.6*20=12 so no of ways to form team 12C4
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Last edited by arvind910619 on 06 Mar 2018, 09:43, edited 1 time in total.
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In how many ways can a coach select a university team from a pool of [#permalink]

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06 Mar 2018, 09:34
Bunuel wrote:
In how many ways can a coach select a university team from a pool of eligible candidates?

(1) The number of eligible candidates is three times greater than the number of slots on the team.
(2) 60% of the 20 athletes are eligible to play on the four-person university team.

Statement 1: if number of team slots is $$n$$, then number number of eligible candidates is $$3n$$

Hence total selection = $$3n_C_n$$. but we don't know the value of $$n$$. Hence Insufficient

Statement 2: Total eligible candidate $$= 60$$%$$*20=12$$

Total members in a team $$=4$$. Hence number of combinations possible = $$12_C_4$$. Sufficient

Option B
In how many ways can a coach select a university team from a pool of   [#permalink] 06 Mar 2018, 09:34
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