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?
Question
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?
Solution
The problem can be solved by using the combination formula which is nCr = n! / r!(n-r)!.
Step 1: Calculate the number of ways to select 3 doctors from the total number of doctors. There are 7 doctors in total (4 men and 3 women). The number of ways to select 3 doctors from 7 is 7C3 = 35.
Step 2: Calculate the number of ways to select 2 lawyers from the total number of lawyers. There are 5 lawyers in total (3 men and 2 women). The number of ways to select 2 lawyers from 5 is 5C2 = 10.
Step 3: Multiply the results of step 1 and step 2 to get the total number of ways to form the committee. So, the total number of ways to form the committee is 35 * 10 = 350.
Therefore, a committee of 5 persons can be formed in 350 ways such that there are 3 doctors and 2 lawyers in the committee.
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