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Joan is allowed to invite 3 of her friends to join her on a family cam

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Bunuel
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Joan is allowed to invite 3 of her friends to join her on a family cam [#permalink] New post   14 Oct 2019, 04:03
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81% (00:40) correct 19% (01:00) wrong based on 137 sessions
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Joan is allowed to invite 3 of her friends to join her on a family camping trip. If Joan has 10 friends, in how many ways can she invite 3 of them?

A. 27
B. 120
C. 140
D. 360
E. 720
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B
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Archit3110
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Re: Joan is allowed to invite 3 of her friends to join her on a family cam [#permalink] New post   15 Oct 2019, 01:20
Bunuel wrote:
Joan is allowed to invite 3 of her friends to join her on a family camping trip. If Joan has 10 friends, in how many ways can she invite 3 of them?

A. 27
B. 120
C. 140
D. 360
E. 720


total possible ways 10c3 ; 120
IMO B
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Kinshook
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Re: Joan is allowed to invite 3 of her friends to join her on a family cam [#permalink] New post   18 Oct 2019, 02:14
Bunuel wrote:
Joan is allowed to invite 3 of her friends to join her on a family camping trip. If Joan has 10 friends, in how many ways can she invite 3 of them?

A. 27
B. 120
C. 140
D. 360
E. 720


Given: Joan is allowed to invite 3 of her friends to join her on a family camping trip.

Asked: If Joan has 10 friends, in how many ways can she invite 3 of them?

10C3 = 10*9*8/3*2*1 = 120

IMO B
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jamalabdullah100
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Joan is allowed to invite 3 of her friends to join her on a family cam [#permalink] New post   12 Dec 2019, 15:21
Archit3110 wrote:
Bunuel wrote:
Joan is allowed to invite 3 of her friends to join her on a family camping trip. If Joan has 10 friends, in how many ways can she invite 3 of them?

A. 27
B. 120
C. 140
D. 360
E. 720


total possible ways 10c3 ; 120
IMO B


Why is it not 10x9x8? I guess it's because arrangement isn't relevant here but how do we know this for sure? Maybe the order in which she invites her friends is relevant?
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Re: Joan is allowed to invite 3 of her friends to join her on a family cam [#permalink] New post   15 Dec 2019, 19:34
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Bunuel wrote:
Joan is allowed to invite 3 of her friends to join her on a family camping trip. If Joan has 10 friends, in how many ways can she invite 3 of them?

A. 27
B. 120
C. 140
D. 360
E. 720


The order in which she invites her friends is of no consequence; hence, we will use combinations instead of permutations. The number of ways to invite 10 friends from 3 is:

10C3 = 10! / (3! x 7!) = (10 x 9 x 8) / 3! = 5 x 3 x 8 = 120.

Answer: B
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Re: Joan is allowed to invite 3 of her friends to join her on a family cam [#permalink] New post   26 Oct 2022, 09:57
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Given that Joan is allowed to invite 3 of her friends to join her on a family camping trip. And we need to find If Joan has 10 friends, in how many ways can she invite 3 of them

We need to select 3 people out of 10. Since its a selection so order does not matter => Combination

=> 10C3 ways = \(\frac{10!}{3!*(10-3)!}\) = \(\frac{10*9*8*7!}{3!*7!}\) = 120

So, Answer will be B
Hope it helps!
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Re: Joan is allowed to invite 3 of her friends to join her on a family cam [#permalink]
26 Oct 2022, 09:57
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