# Statistics Discussion response combinatorial numbers equation

*label*Mathematics

*timer*Asked: Jan 4th, 2019

*account_balance_wallet*$10

### Question Description

Suppose that a class contains 15 boys and 30 girls and that ten students are to be selected at random for a particular assignment. Find the probability that exactly 3 boys will be chosen.

The question above represents a scenario that may require the application of the combination rule. The combination rule involves the situation in which one finds the most appropriate way that they can select r objects from a population of n subjects following no definite order. Through this approach, one can utilize the given information and generate the provided components to help in making a decision.

In this case, the formula to use is nCr=n! / (n-r)! r!

The selection will involve 3 boys and 7 girls.

In that case, (15C3* 30C7)/ 45C10

The combination of 15 and 3 will give;

15C3=15!/ ((15-3)!3! = 455. This case represents the various ways that a researcher can successfully select 3 boys from a population of 15 boys

30C7=30! / ((30-7)!7!)=2035800. This representation offers the various approaches that one can obtain 7 girls from a population containing 30 girls.

45C10=45! / ((45-10)! 10!)= 3190187800. This equation represents the multiple ways that one can select 10 students (both boys and girls) from a population containing 45 students.

In the attempt to obtain 3 boys from a selection containing 10 students, one needs to look for the product of the combination of 7 girls and 3 boys. The researcher may then need to look for the quotient of the above mixture and the combination of total students.

In this case, 455*2035800=926289000

By division we get, 926289000/ 3190187800= 0.29030

Thus the probability of obtaining 3 boys from a selection of 10 students= 0.2903 or 29.03

Follow up question from the instructor:

Did you use a calculator with a nCr button or Excel?

Why do you calculate (15C3* 30C7)/ 45C10 ? Why do you multiply and divide these combinations?

## Tutor Answer

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