## How many ways are there to put the balls into the boxes?

## How many ways are there to put the balls into the boxes?

How many ways are there to place the balls into the boxes? There are only six ways.

## How many ways can you distribute 4 balls into 5 boxes?

If there was no restriction; the distribution of 4 distinguishable balls among 5 boxes could have been done in (5 * 5 * 5 * 5) ways = 625 ways.

**How many ways 5 balls can be placed in 3 boxes such that no box remains empty?**

* Now you have ensured that no box remains empty. * Now, every ball can be placed in boxes in three different ways. Hence, the total no. of ways of placing the rest 5 balls is 3*3*3*3*3=243.

### How many ways can group N objects in K box?

So the answer is 9. Distributing n indistinguishable objects into k indistinguishable boxes is the same as writing n as a sum of at most k positive integers in non-increasing order. There is no simple closed formula for this number.

### How many ways can n balls be put into 5 boxes if no box has exactly 2 balls?

Total ways of putting 5 balls in five distinct boxes = (5^5) = 3125. Ways of choosing two empty distinct boxes = 5×4= 20. Next, ways of putting one ball each in 3 remaining boxes = 3×2×1=6. Ways to put remaining 2 balls in any of above 3 boxes = 3×3=9.

**How many ways can you put 3 balls in 4 boxes?**

Each ball can be put into any one of the 3 boxes, independently of where the other balls are. There are 3*3*3*3 = 81 ways of doing this.

## How many ways can we pick any number of balls from a pack of 3 different balls?

Now, you can easily calculate the no. of ways to choose 3 balls as follows: 28+21+15+10+6+3+1= 84.

## How many ways to distribute 5 balls into 3 boxes if each box must have at least one ball in it if?

We have to distribute 5 distinct balls into 3 identical boxes. Thus, n = 5 and k = 3. Therefore, there are a total of 41 possibilities.

**What is the number of ways in which you can distribute 5 balls in 3 boxes when?**

As there are 5 balls and three boxes each ball has 3 choices. So to answer is 3x3x3x3x3=243.

### How many ways are there of distributing n identical balls among K boxes?

If we are supposed to distribute k distinct objects to n identical recipients so that each gets at most one, we cannot do so if k>n, so there are 0 ways to do so. On the other hand, if k≤n, then it doesn’t matter which recipient gets which object, so there is only one way to do so.

### How many ways can group N items be?

The total number of ways that the parts can be selected is 4×3×5×4 or 240 ways. Factorial Notation: the notation n! (read as, n factorial) means by definition the product: n!