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A student council must select a two-person welcoming committee and a t

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Bunuel
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A student council must select a two-person welcoming committee and a t [#permalink] New post   31 Jul 2022, 10:00
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A student council must select a two-person welcoming committee and a three-person planning committee from among its members. There are exactly 10 ways to select a two-person team for the welcoming committee. It is possible for students to serve on both committees. In how many different ways can a three-person planning committee be selected?

(A) 10
(B) 12
(C) 15
(D) 18
(E) 25
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gokul5544
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Re: A student council must select a two-person welcoming committee and a t [#permalink] New post   01 Aug 2022, 08:41
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Given : nC2 = 10 , gives us n=5

Need to find 5C3 which is equal to 10.
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Shane04
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Re: A student council must select a two-person welcoming committee and a t [#permalink] New post   26 May 2023, 22:04
gokul5544 wrote:
Given : nC2 = 10 , gives us n=5

Need to find 5C3 which is equal to 10.



Can you explain how do we calculate n from Nc2=10
I understood what I had to do but didn't know how to reverse calculate
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Champer21
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Re: A student council must select a two-person welcoming committee and a t [#permalink] New post   20 Jan 2024, 07:40
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Shane04 wrote:
gokul5544 wrote:
Given : nC2 = 10 , gives us n=5

Need to find 5C3 which is equal to 10.



Can you explain how do we calculate n from Nc2=10
I understood what I had to do but didn't know how to reverse calculate


I did it in the following way:
NC2
N/2 = 10 l *2
N = 20

and to get 20 we multiplicate two number because we choose two numbers.
you can either choose 10*2 or 20*1 but because of the formula you need consecutively reducing numbers: 5*4 = N.

To make it clear, I want to show the back solve
N=5
NC2

5*4/2! = 10
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Re: A student council must select a two-person welcoming committee and a t [#permalink]
20 Jan 2024, 07:40
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