Problem Solving

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

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. For more information about the FCP, watch our free video: https://www.gmatprepnow.com/module/gmat- ... /video/775

You can also watch a demonstration of the FCP in action: https://www.gmatprepnow.com/module/gmat ... /video/776

Then you can try solving the following questions:

EASY
- https://www.beatthegmat.com/what-should- ... 67256.html
- https://www.beatthegmat.com/counting-pro ... 44302.html
- https://www.beatthegmat.com/picking-a-5- ... 73110.html
- https://www.beatthegmat.com/permutation- ... 57412.html
- https://www.beatthegmat.com/simple-one-t270061.html


MEDIUM
- https://www.beatthegmat.com/combinatoric ... 73194.html
- https://www.beatthegmat.com/arabian-hors ... 50703.html
- https://www.beatthegmat.com/sub-sets-pro ... 73337.html
- https://www.beatthegmat.com/combinatoric ... 73180.html
- https://www.beatthegmat.com/digits-numbers-t270127.html
- 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

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

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.

Answer: C