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A shipping company has four empty trucks that will head out in the mor

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A shipping company has four empty trucks that will head out in the mor  [#permalink]

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New post 17 Mar 2015, 05:47
2
6
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

57% (01:41) correct 43% (02:27) wrong based on 110 sessions

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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


Kudos for a correct solution.

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Re: A shipping company has four empty trucks that will head out in the mor  [#permalink]

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New post 17 Mar 2015, 09:07
2
each box have 4 options to place
so 4^4=256
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Re: A shipping company has four empty trucks that will head out in the mor  [#permalink]

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New post 23 Mar 2015, 03:55
Bunuel 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


Kudos for a correct solution.


MAGOOSH OFFICIAL SOLUTION:

Where we put one box has absolutely no bearing on where we put any of the other boxes. The placement of the four boxes is completely independent of one another. For each box, we have four choices.

N = 4*4*4*4 = 16*16 = 256

Answer = (C)
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Re: A shipping company has four empty trucks that will head out in the mor  [#permalink]

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New post 21 Nov 2018, 08:27
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Bunuel 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


Take the task of shipping the 4 boxes and break it into stages.

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

Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.

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Re: A shipping company has four empty trucks that will head out in the mor   [#permalink] 21 Nov 2018, 08:27
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