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From a group of 8 people, it is possible to create exactly 56 differen

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Bunuel
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From a group of 8 people, it is possible to create exactly 56 differen [#permalink] New post   27 May 2019, 03:35
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72% (01:17) correct 28% (01:11) wrong based on 87 sessions
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From a group of 8 people, it is possible to create exactly 56 different k-person committees. Which of the following could be the value of k?

I. 3
II. 5
III. 7

A. I only
B. II only
C. III only
D. I and II only
E. I, II and III
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D
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firas92
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From a group of 8 people, it is possible to create exactly 56 differen [#permalink] New post   Updated on: 27 May 2019, 03:50
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8Ck = 56

Note that nCk = nC(n-k)

Therefore 8C3=8C5 (=56), whereas 8C7=8

Only I and II are possible

Answer is (D)

Hit Kudos if this helped!

Originally posted by firas92 on 27 May 2019, 03:41.
Last edited by firas92 on 27 May 2019, 03:50, edited 1 time in total.
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Re: From a group of 8 people, it is possible to create exactly 56 differen [#permalink] New post   27 May 2019, 03:44
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Bunuel wrote:
From a group of 8 people, it is possible to create exactly 56 different k-person committees. Which of the following could be the value of k?

I. 3
II. 5
III. 7

A. I only
B. II only
C. III only
D. I and II only
E. I, II and III


8CK = 56, let's check if k=3?
8C3 = (8!)/(5!)(3!) = 86, perfect.

Also k can be 5 because nCr = nC(n-r)

Can k be 7? No 8C7= 8.

Answer: D. I and II only
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Re: From a group of 8 people, it is possible to create exactly 56 differen [#permalink] New post   27 May 2019, 05:16
Bunuel wrote:
From a group of 8 people, it is possible to create exactly 56 different k-person committees. Which of the following could be the value of k?

I. 3
II. 5
III. 7

A. I only
B. II only
C. III only
D. I and II only
E. I, II and III


use combinatrics to solve the question :
answer options are the clue to solve
8c3=8c5=56
IMO D
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ankitprad
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Re: From a group of 8 people, it is possible to create exactly 56 differen [#permalink] New post   13 Sep 2019, 06:21
8Ck= 56
8! / k!* (8-k)! = 56
8! = 56 * k! ( 8-k) !
8*7*6! = 56 * k! ( 8-k) !
6!=k! ( 8-k) !

Use answer options :

1 ) 720 = 3! * ( 8-3)!
720 = 6*5! = 6* 120

Option I is correct

2) If k is 5 then , 5! * (3)! = 720

Option II is correct

3) If k is 7 then , 7! * (1)! = 5040
Option III is incorrect

Hence, I & II
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Re: From a group of 8 people, it is possible to create exactly 56 differen [#permalink]
13 Sep 2019, 06:21
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