Combinations with Repetitions Formulae

In this class, We discuss Combinations with Repetitions Formulae.

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We take an example and understand combinations with repetitions formulae.

First, we take an example and understand where combinations with repetitions apply.

In a shop, there are three types of soda available.

The three types of soda are given below.

1) Pepsi

2) Coke

3) Thums up

Ten people came to a shop, and they wanted to buy soda.

What is the number of ways they select soda?

Here, repetitions are allowed.

All ten members can select Coke.

Only some members can select Coke, and the remaining can select Pepsi.

Ten persons are going to select three types of soda.

Assumption unlimited soda is available.

We have Coke | Pepsi | Thums up

N types of soda are available. In our example, N = 3.

X selections are made. In our example, X = 10.

The below diagram shows different types of selections.

To separate the types of soda, we have standing lines.

Three types of soda are separated using two lines.

N types are separated using N-1 lines.

The arrangement of the above is our different selections.

The above arrangement is done in (X + N -1)!/(X! N-1!)

The above formulae are the same as X+N-1 C X.

The Formulae for combinations with repetitions is given as X+N-1 C X