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In how many ways can we put 4 different balls in 3 different boxes whe
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06 Jul 2022, 03:09
06 Jul 2022, 03:09
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Question Stats:
55% (00:48) correct
44% (01:21) wrong based on 9 sessions
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In how many ways can we put 4 different balls in 3 different boxes when any box can contain any number of balls?
A. 80
B. 81
C. 64
D. 63
E. 82
A. 80
B. 81
C. 64
D. 63
E. 82
Part of the project: GRE QCQ & PS 3 Questions Every One DAILY Challenge - (2022)
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GRE Math Essentials (2022)
GRE Geometry Formulas for a Q170
GRE - Math Book
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GRE Math Essentials (2022)
GRE Geometry Formulas for a Q170
GRE - Math Book
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Re: In how many ways can we put 4 different balls in 3 different boxes whe
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06 Jul 2022, 07:21
06 Jul 2022, 07:21
1
Carcass wrote:
In how many ways can we put 4 different balls in 3 different boxes when any box can contain any number of balls?
A. 80
B. 81
C. 64
D. 63
E. 82
A. 80
B. 81
C. 64
D. 63
E. 82
Take the task of distributing the 4 different balls and break it into stages.
Stage 1: Select a box for the 1st ball to go into.
There are 3 available boxes, so we can complete stage 1 in 3 ways
Stage 2: Select a box for the 2nd ball to go into.
There are 3 available boxes, so we can complete stage 2 in 3 ways
Stage 3: Select a box for the 3rd ball to go into.
There are 3 available boxes, so we can complete stage 3 in 3 ways
Stage 4: Select a box for the 4th ball to go into.
There are 3 available boxes, so we can complete stage 4 in 3 ways
By the Fundamental Counting Principle (FCP), we can complete all 4 stages (and thus distribute all 4 balls) in (3)(3)(3)(3)(4) ways (= 81 ways)
Answer: B
gmatclubot
Re: In how many ways can we put 4 different balls in 3 different boxes whe [#permalink]
06 Jul 2022, 07:21
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