Question

# The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is-

- 5
- 21
- 3
^{8}
^{8}C_{3}

^{8}^{8}C_{3}Hint:

### By choosing some items from a set and creating subsets, permutation and combination are two approaches to represent a group of objects. It outlines the numerous configurations for a particular set of data. Permutations are the selection of data or objects from a set, whereas combinations are the order in which they are represented. Here we have to find the number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty.

## The correct answer is: 21

### A permutation is the non-replaceable selection of r items from a set of n items in which the order is important.

A combination is created by selecting r items from a group of n items without replacing them and without regard to their order.

Here we have given the word as: MISSISSIPPI.

Here we have to find the number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty. So:

I = 4 times,

S= 4 times,

P = 2 times,

M= 1 time

So the number of words will be:

The different ways in which items from a set may be chosen, usually without replacement, to construct subsets, are called permutations and combinations. When the order of the selection is a consideration, this selection of subsets is referred to as a permutation; when it is not, it is referred to as a combination. So the final answer is 21.

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### If ^{n}C_{r} denotes the number of combinations of n things taken r at a time, then the expression ^{n}C_{r+1} + ^{n}C_{r –1} + 2 × ^{n}C_{r} equals-

The different ways in which items from a set may be chosen, usually without replacement, to construct subsets, are called permutations and combinations. When the order of the selection is a consideration, this selection of subsets is referred to as a permutation; when it is not, it is referred to as a combination. So the final answer is .

### If ^{n}C_{r} denotes the number of combinations of n things taken r at a time, then the expression ^{n}C_{r+1} + ^{n}C_{r –1} + 2 × ^{n}C_{r} equals-

The different ways in which items from a set may be chosen, usually without replacement, to construct subsets, are called permutations and combinations. When the order of the selection is a consideration, this selection of subsets is referred to as a permutation; when it is not, it is referred to as a combination. So the final answer is .