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# If there are 16 people to choose from, what is the ratio of the number

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Math Expert
Joined: 02 Sep 2009
Posts: 52431
If there are 16 people to choose from, what is the ratio of the number  [#permalink]

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21 Jan 2018, 02:24
00:00

Difficulty:

15% (low)

Question Stats:

85% (01:30) correct 15% (02:03) wrong based on 60 sessions

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If there are 16 people to choose from, what is the ratio of the number of possible 7-person committees to the number of possible 8-person committees?

(A) 7:8
(B) 8:7
(C) 7:9
(D) 8:9
(E) 9:8

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If there are 16 people to choose from, what is the ratio of the number  [#permalink]

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21 Jan 2018, 02:35
Bunuel wrote:
If there are 16 people to choose from, what is the ratio of the number of possible 7-person committees to the number of possible 8-person committees?

(A) 7:8
(B) 8:7
(C) 7:9
(D) 8:9
(E) 9:8

Number of ways of selecting $$7$$ people out of $$16$$ people $$=16_C_7$$

Number of ways of selecting $$8$$ people out of $$16$$ people $$=16_C_8$$

Hence the ratio $$= \frac{16_C_7}{16_C_8}=\frac{8}{9}$$

Option D
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Re: If there are 16 people to choose from, what is the ratio of the number  [#permalink]

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21 Jan 2018, 04:12
16C7 divided by 16C8= 8:9.
Hence D
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Re: If there are 16 people to choose from, what is the ratio of the number  [#permalink]

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21 Jan 2018, 04:18
What if each committee member is assigned a different role? Say, finance member, technical member, etc. Doesn't the combination become permutation in this case since even the order and thus the role in the committee shall also matter?
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Re: If there are 16 people to choose from, what is the ratio of the number  [#permalink]

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21 Jan 2018, 04:21
tush1992 wrote:
What if each committee member is assigned a different role? Say, finance member, technical member, etc. Doesn't the combination become permutation in this case since even the order and thus the role in the committee shall also matter?

The word clearly says choose and not assign different roles. So as per me it should be combination since order and assignment does not matter
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Re: If there are 16 people to choose from, what is the ratio of the number  [#permalink]

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21 Jan 2018, 04:43
globaldesi wrote:
tush1992 wrote:
What if each committee member is assigned a different role? Say, finance member, technical member, etc. Doesn't the combination become permutation in this case since even the order and thus the role in the committee shall also matter?

The word clearly says choose and not assign different roles. So as per me it should be combination since order and assignment does not matter

That seems like the most possible explanation. Also, even if its a permutation, the answer is still 8:9 (So awfully stupid of me. Should have calculated this earlier).
Re: If there are 16 people to choose from, what is the ratio of the number &nbs [#permalink] 21 Jan 2018, 04:43
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