A shipping company has four empty trucks that will head out in the morning, all four to the same destination. The clerk has four different boxes to ship to that same destination. All four boxes could go on any one of the trucks, or the boxes could be split up into any groupings and given to the trucks in any combinations (ie. two to one truck, one to another, and one to another). In how many different ways could the boxes be put on the four trucks?
(A) 16
(B) 64
(C) 256
(D) 576
(E) 4096
OA C
Source: Magoosh
A shipping company has four empty trucks that will head out
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Take the task of shipping the 4 boxes and break it into stages.BTGmoderatorDC wrote:A shipping company has four empty trucks that will head out in the morning, all four to the same destination. The clerk has four different boxes to ship to that same destination. All four boxes could go on any one of the trucks, or the boxes could be split up into any groupings and given to the trucks in any combinations (ie. two to one truck, one to another, and one to another). In how many different ways could the boxes be put on the four trucks?
(A) 16
(B) 64
(C) 256
(D) 576
(E) 4096
OA C
Source: Magoosh
Let's call the 4 boxes A, B, C and D
Stage 1: Select a truck to ship box A in
There are 4 trucks from which to choose, so we can complete stage 1 in 4 ways
Stage 2: Select a truck to ship box B in
There are 4 trucks from which to choose, so we can complete this stage in 4 ways
Stage 3: Select a truck to ship box C in
There are 4 trucks from which to choose, so we can complete this stage in 4 ways
Stage 4: Select a truck to ship box D in
There are 4 trucks from which to choose, so we can complete this stage in 4 ways
By the Fundamental Counting Principle (FCP), we can complete all 4 stages (and thus ship all 4 boxes) in (4)(4)(4)(4) ways (= 256 ways)
Answer: C
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EASY
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MEDIUM
- https://www.beatthegmat.com/combinatoric ... 73194.html
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- https://www.beatthegmat.com/doubt-on-sep ... 71047.html
- https://www.beatthegmat.com/combinatoric ... 67079.html
DIFFICULT
- https://www.beatthegmat.com/wonderful-p- ... 71001.html
- https://www.beatthegmat.com/permutation- ... 73915.html
- https://www.beatthegmat.com/permutation-t122873.html
- https://www.beatthegmat.com/no-two-ladie ... 75661.html
- https://www.beatthegmat.com/combinations-t123249.html
Cheers,
Brent
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Since each box has 4 options for which truck it will be put on to, 4 boxes will have 4 x 4 x 4 x 4 = 256 options how they are put on the trucks.BTGmoderatorDC wrote:A shipping company has four empty trucks that will head out in the morning, all four to the same destination. The clerk has four different boxes to ship to that same destination. All four boxes could go on any one of the trucks, or the boxes could be split up into any groupings and given to the trucks in any combinations (ie. two to one truck, one to another, and one to another). In how many different ways could the boxes be put on the four trucks?
(A) 16
(B) 64
(C) 256
(D) 576
(E) 4096
OA C
Source: Magoosh
Answer: C
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