Hey Developer’s, I’m back with a new topic which is Multinomial Coefficients in the series of statistics foundations.

### Quick Refresher

A binomial coefficient equals the number of combinations of k items that can be selected from a set of n items.

So, let’s get started …

### Multinomial Coefficients

It’s not just of separating two group of elements but actually separating several groups ,more than 2

Example: 10 students need to from 3 groups consisting of 4,3 and 3 members repectively.How many ways can students be assigned to these groups ?

Solution = First Group : Choose 4 students out of 10, 10**C**4 arrangements.

We are left with 6 students: number of ways to split them is 6**C**3

(10**C**4)(6**C**3) = (10!/4!6!) * (6!/3!3!) = 10!/4!3!3! = 4200

**Multinomial Coefficient written as **

**Just like the binomial coefficients,**

Example 1: Picking 4,3,3 students out of 10 : (10** C** 4,3,3) = 10!/4!3!3! = 4200

Example 2: Number of ways to arrange 3 a’s, 4 b’s and 5 c’s is : (12 **C** 3,4,5) = 12!/3!4!5! = 27,720

#### Next Post will be on Probability of a union of events

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