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# A basketball team has 11 players on its roster. Only 5 players can be

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Math Expert
Joined: 02 Sep 2009
Posts: 58458
A basketball team has 11 players on its roster. Only 5 players can be  [#permalink]

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26 Jul 2019, 00:28
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15% (low)

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74% (00:50) correct 26% (00:51) wrong based on 66 sessions

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A basketball team has 11 players on its roster. Only 5 players can be on the court at one time. How many different groups of 5 players can the team put on the floor?

(A) 5^11
(B) 11C5
(C) 11P5
(D) 11^5
(E) 11!*5!

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Re: A basketball team has 11 players on its roster. Only 5 players can be  [#permalink]

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26 Jul 2019, 07:19
Bunuel wrote:
A basketball team has 11 players on its roster. Only 5 players can be on the court at one time. How many different groups of 5 players can the team put on the floor?

(A) 5^11
(B) 11C5
(C) 11P5
(D) 11^5
(E) 11!*5!

total ways ; 11*10*9*8*7 ; or say 11P5 ways
IMO C
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Re: A basketball team has 11 players on its roster. Only 5 players can be  [#permalink]

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28 Jul 2019, 08:17
Bunuel wrote:
A basketball team has 11 players on its roster. Only 5 players can be on the court at one time. How many different groups of 5 players can the team put on the floor?

(A) 5^11
(B) 11C5
(C) 11P5
(D) 11^5
(E) 11!*5!

we want to look for different combinations of teams, so we choose an answer with "C" for combination
we have 11 players in total of which only 5 can play in one team. This leads us to the formula
11!/5!(11-5)!
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A basketball team has 11 players on its roster. Only 5 players can be  [#permalink]

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09 Oct 2019, 07:48
A basketball team has 11 players on its roster. Only 5 players can be on the court at one time. How many different groups of 5 players can the team put on the floor?

(A) 5^11
(B) 11C5
(C) 11P5
(D) 11^5
(E) 11!*5!

Now since ,we want the number of different groups of five which can be formed. Other doesn’t matter

Say group consist of players (a,b,c,d,e) = Group with players (b,c,d,e,a)= (c,b,a,e,d)
So definitely a combination question
.: 11 choose 5 = 11C5 = 11C6

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Re: A basketball team has 11 players on its roster. Only 5 players can be  [#permalink]

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09 Oct 2019, 10:29
Staphyk Bunuel OA is B, but shouldn't this be a permutation problem? If the 11 players are a, b, c, d, e, f, g, h, i, j, and k. A 5-player team of a,b,c,d, and e will be different from a team that contains f, g, h, i, and j, etc. Please clarify.

Thanks.
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A basketball team has 11 players on its roster. Only 5 players can be  [#permalink]

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09 Oct 2019, 10:52
1
You are not wrong there; however, when we say order doesn’t matter we mean the ordering of elements of a particular group never results in a distinct combination to be accounted for.
Example here to batress my point ,Say you have 5 players: (Bunuel,bb,Staphyk,Nightblade,and bebs)
You want to create different groups of three for an upcoming Naija olympics (made up Lolx)
Now a group of (Staphyk,bebs,Bunuel) is no different form a group of (Bunuel,Staphyk,bebs) just re-arranged them

Difference only comes when we have a group of (Staphyk,bb,bebs) or (Bunuel,bb,Nightblade) etc.

That is why it was question .
combination
**Had the question been how many distinct members of group of 5 players**
Then we would have gone for permutations

Hope it’s clear. I hope my boss Bunuel will add up
bebs wrote:
Staphyk Bunuel OA is B, but shouldn't this be a permutation problem? If the 11 players are a, b, c, d, e, f, g, h, i, j, and k. A 5-player team of a,b,c,d, and e will be different from a team that contains f, g, h, i, and j, etc. Please clarify.

Thanks.

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A basketball team has 11 players on its roster. Only 5 players can be   [#permalink] 09 Oct 2019, 10:52
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# A basketball team has 11 players on its roster. Only 5 players can be

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