Out of 10 men, there are 4 doctors, 3 teachers and 3 lawyers and out of 8 women, there are 3 doctors, 3 dancers and 2 lawyers. In how many ways can a committee of 5 persons be formed such that , There are 3 doctors and 2 lawyers in the committee?Options7C3 x 5C210C5 x 8C57C5 x 5C510C7 x 8C5

The problem is asking for the number of ways to form a committee of 5 people with 3 doctors and 2 lawyers.

First, let's find the total number of doctors and lawyers. There are 4 male doctors and 3 female doctors, so there are 7 doctors in total. There are 3 male lawyers and 2 female lawyers, so there are 5 lawyers in total.

We want to choose 3 doctors out of 7 and 2 lawyers out of 5.

The number of ways to choose 3 doctors out of 7 is given by the combination formula "7 choose 3", which is denoted as 7C3.

Similarly, the number of ways to choose 2 lawyers out of 5 is given by the combination formula "5 choose 2", which is denoted as 5C2.

The total number of ways to form the committee is the product of these two quantities, because for each way to choose the doctors, there are multiple ways to choose the lawyers.

So, the answer is 7C3 x 5C2.