## Introduction

Combinatorics is the branch of mathematics that deals with arrangements of a set of objects, given a set of conditions. If an operation consists of two steps, of which the first can be done in n_{1} ways and for each of these the second can be done in n_{2} ways, then the number of ways of doing both steps is:

_{1}* n

_{2}

If an operation consists of k steps, of which the first can be done in n_{1} ways and for each of these the second step can be done in n_{2} ways, for each of these the third step can be done in n_{3} ways and so forth, then the number of ways of doing all steps is:

_{1}* n

_{2}* n

_{3}* n

_{4}* . . . * n

_{k}

## Use

### Example

The number of different outfits that can be assembled from 4 pairs of trousers and 6 jumpers is:

### Example

An item is to be chosen from each of four different bins containing 4, 3, 5 and 4 items respectively. The total number of ways that the items can be selected is: