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

Question

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.

(A) 16
(B) 64
(C) 256
(D) 576
(E) 4096

arunshankarkkkk · Answer

each box have 4 options to place 
 so 4^4=256

Bunuel · Answer

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)

BrentGMATPrepNow · Answer

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.

RELATED VIDEOS
 https://www.youtube.com/watch?v=w5d5bvCRyd4

https://www.youtube.com/watch?v=_PFBp2BoMUY

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards