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# How many ways can 4 prizes be given away to 3 boys, if each boy is eli

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Math Expert
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How many ways can 4 prizes be given away to 3 boys, if each boy is eli  [#permalink]

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18 Sep 2019, 05:13
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Difficulty:

55% (hard)

Question Stats:

44% (01:07) correct 56% (01:02) wrong based on 36 sessions

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How many ways can 4 different prizes be given away to 3 boys, if each boy is eligible for all the prizes?

A. 81
B. 64
C. 48
D. 27
E. 12

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Re: How many ways can 4 prizes be given away to 3 boys, if each boy is eli  [#permalink]

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18 Sep 2019, 05:21
Let the prizes be A, B, C & D

A can be given to Boy 1 or Boy 2 or Boy 3 - 3 Options
B can be given to Boy 1 or Boy 2 or Boy 3 - 3 Options
C can be given to Boy 1 or Boy 2 or Boy 3 - 3 Options
D can be given to Boy 1 or Boy 2 or Boy 3 - 3 Options

Therefore the total number of outcomes is 3*3*3*3=81

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Re: How many ways can 4 prizes be given away to 3 boys, if each boy is eli  [#permalink]

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18 Sep 2019, 06:37
How many ways can 4 different prizes be given away to 3 boys, if each boy is eligible for all the prizes?

A. 81
B. 64
C. 48
D. 27
E. 12[/quote]

Each boy(3) is eligible for all the 4 different prizes. So no of ways 3^4 = 81
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Re: How many ways can 4 prizes be given away to 3 boys, if each boy is eli  [#permalink]

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18 Sep 2019, 07:55
Bunuel wrote:
How many ways can 4 different prizes be given away to 3 boys, if each boy is eligible for all the prizes?

A. 81
B. 64
C. 48
D. 27
E. 12

1st prize can be given in 3 ways
2nd prize can be given in 3 ways
3rd prize can be given in 3 ways
4th prize can be given in 3 ways

Total no of ways of distribution of 4 prizes is 3*3*3*3 = 81, Answer must be (A)
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Re: How many ways can 4 prizes be given away to 3 boys, if each boy is eli  [#permalink]

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23 Sep 2019, 09:37
Bunuel wrote:
How many ways can 4 different prizes be given away to 3 boys, if each boy is eligible for all the prizes?

A. 81
B. 64
C. 48
D. 27
E. 12

Since each prize can have 3 choices (a boy being a choice), the 4 prizes can be given to 3 boys in
3 x 3 x 3 x 3 = 3^4 = 81 ways.

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Re: How many ways can 4 prizes be given away to 3 boys, if each boy is eli  [#permalink]

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23 Sep 2019, 09:45
Each price is having 3 contenders, so total no of ways will be 3*3*3*3 = 3^4=81
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Re: How many ways can 4 prizes be given away to 3 boys, if each boy is eli   [#permalink] 23 Sep 2019, 09:45
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