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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
Posts: 64144
In how many ways can a coach select a university team from a pool of  [#permalink]

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06 Mar 2018, 06:18
00:00

Difficulty:

15% (low)

Question Stats:

76% (01:02) correct 24% (00:58) wrong based on 276 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.

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

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Updated on: 06 Mar 2018, 08:43
2
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

Originally posted by arvind910619 on 06 Mar 2018, 08:29.
Last edited by arvind910619 on 06 Mar 2018, 08:43, 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, 08:34
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
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Re: In how many ways can a coach select a university team from a pool of  [#permalink]

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01 Jan 2019, 19:01
In how many ways can a coach select a 4-person university team from a pool of eligible candidates?

1) The number of eligible candidates is three times as great as the number of slots on the team.
Given that coach select a 4-person university team, implies number of slots = 4
number of eligible candidates is three times as great as the number of slots on the team => eligible candidates = 3(number of slots) + number of slots
= 3(4) +4
=12
Number of ways we can select a team of 4 number = $$12C4$$
Sufficient

2) 60% of the 20 athletes are eligible to play on the four-person university team.
60% of 20 athletes = 0.6*20
= 12
Number of ways we can select a team of 4 number = $$12C4$$
Sufficient

Option D is correct
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Joined: 03 Feb 2017
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Re: In how many ways can a coach select a university team from a pool of  [#permalink]

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20 Jan 2019, 02:48
1
Dare Devil wrote:
In how many ways can a coach select a 4-person university team from a pool of eligible candidates?

1) The number of eligible candidates is three times as great as the number of slots on the team.
Given that coach select a 4-person university team, implies number of slots = 4
number of eligible candidates is three times as great as the number of slots on the team => eligible candidates = 3(number of slots) + number of slots
= 3(4) +4
=12
Number of ways we can select a team of 4 number = $$12C4$$
Sufficient

2) 60% of the 20 athletes are eligible to play on the four-person university team.
60% of 20 athletes = 0.6*20
= 12
Number of ways we can select a team of 4 number = $$12C4$$
Sufficient

Option D is correct

The part "choose a 4-member university team" is nowhere to be found in the ordinary question. So B is correct
Re: In how many ways can a coach select a university team from a pool of   [#permalink] 20 Jan 2019, 02:48