Question

In how many ways can 9 female and 7 male members be selected for a review team from a group of 15 females and 10males

Answer 1

Answer:

9450 ways

Step-by-step explanation:

Assuming the female reviewers select females and males the same.

15*9 = 135

7*10 = 70

70*135 = 9450 possible ways that the 9 female and 7 male members can be selected.

Answer 2

Given,

There are 15 females and 10 males.

To find,

The number of ways by which we can select 9 females and 7 males from 15 females and 10 males for a review team.

Solution,

The number of ways by which we can select 9 females and 7 males from 15 females and 10 males for a review team is 6,00,600.

We can simply solve the mathematical question by the following process.

We know by Permutation and Combination that for selecting x objects from a bunch of n objects, we use combinations. Mathematically, it can be written as ⁿCₓ.

Combinations are used when we just have to select the objects. Permutations are used to select as well as arrange the objects.

Now,

We are given that there are 15 females and 10 males.

Thus,

The number of ways by which we can select 9 females and 7 males from 15 females and 10 males for a review team is as follows;

⇒ ¹⁵C₉ x ¹⁰C₇

⇒ $\frac{15!}{9!* 6!} *\frac{10!}{7!*3!}$

⇒ $\frac{10.11.12.13.14.15}{1.2.3.4.5.6} * \frac{8.9.10}{1.2.3}$

⇒ 4 x 3 x 10 x 5 x 11 x 13 x 7

⇒ 6,00,600

As a result, there are 6,00,600 ways to do the task.