In how many of ways can 5 balls be placed in 4 tins if any number of b

Question

In how many of ways can 5 balls be placed in 4 tins if any number of balls can be placed in any tin?

(A)  5  C  4

(B)  5  P  4

(C)  5^4

(D)  4^5

(E)  5^5

Source:  Nova GMAT

nehasomani33 · Answer

If we have 4 destinations and 5 balls to arrange, shouldn't it be 5*5*5*5?

saratsuman · Answer

Here's what I can understand from the given stem.

"We have 5 balls that are to be placed into 4 tins and any number of balls can be placed in a tin"

Therefore, we have 5 balls   and 4 tins

No of ways B1 can be placed into a tin = 4  ;
No of ways B2 can be placed into a tin = 4  ;
No of ways B3 can be placed into a tin = 4  ;
No of ways B4 can be placed into a tin = 4  ;
No of ways B5 can be placed into a tin = 4  ;

Therefore, we can place 5 balls into 4 tins in 4*4*4*4*4 ways => 4^5 ways.

Hope it's clear.

ScottTargetTestPrep · Answer

Since each ball has 4 choices of tins to be placed in, the number of ways 5 balls can be placed in 4 tins is 4 x 4 x 4 x 4 x 4 = 4^5.

In other words, Ball 1 can go into any of the 4 tins, so it has 4 choices. Ball 2 can go into any of the 4 tins, so it also has 4 choices. Similarly, Ball 3 has 4 choices, Ball 4 has 4 choices, and Ball 5 has 4 choices. Thus, the total number of choices for the 5 balls is 4 x 4 x 4 x 4 x 4 = 4^5.

Answer: D

miag · Answer

hi, can someone explain the difference between 5^4, and 4^5 here?  Bunuel   Sajjad1994

Bunuel · Answer

We are assigning balls to tins, assigning tins to balls makes no sense.

We are placing 5 balls into 4 tins, and any number of balls can go into any tin.

So for each ball, there are 4 choices (any of the 4 tins).

Total number of ways = 4 * 4 * 4 * 4 * 4 = 4^5

Answer: D.

Gimmy · Answer

Hi  Bunuel

I come across another question where it mentioned that there are 8 chocolates and 3 children. How many ways can you distribute the chocolates to the children. The solution I get was to use the stars and bars method where (8+3-1)C(3-1) = 10C2 = 45. How is this question different where I cannot use the same method ie (5+4-1)C(4-1) = 8C3 = 56. There is also no clear indication in the question that the balls are indistinguishable.

Wazzzaa · Answer

Have the same doubt, could anyone please explain this?

Wazzzaa · Answer

What I'm I doing wrong ?

My approach:

The ways of distributing 5 balls in four bins:

Total ways = 4 + 4 + 12 + 12 + 12 + 12 = 56.

Bunuel · Answer

In the question, the balls are distinct, so for each case in your list, you'd need to multiply by the number of ways to assign specific balls to that distribution. You're counting distributions of counts, not actual assignments of distinct balls.

In how many of ways can 5 balls be placed in 4 tins if any number of b

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

In how many of ways can 5 balls be placed in 4 tins if any number of b

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