Please could someone explain this in details Thanks Let me t

Please could someone explain this in details Thanks!

Let me tell you a little dirty secret about the mutual dislike between mathematicians and physicists. It can escalate into a full blown war if diplomacy is not attempted properly.

    It happens that a graduate student in theoretical/mathematical physics is looking for five members of his dissertation committee. He has been working closely with three professors in the mathematics department, and 5 professors in the physics department on his dissertation research.

    Now comes the monkey wrench.

    For comic relief, can you figure out how may ways can this hapless graduate student can choose among his beloved professors if the chair of the committee must be a mathematician, and the rest of the committee can be a mix of mathematicians and physicists?

Solution

Number of mathematicians = 3

Number of physicts = 5

Committe must have 5 memeber.

The chair of the committe should be mathematician which can be chosen in 3C₁ ways

Number of members remaining is (5+3-1) from whome the remaining 4 member should be selected which can be d one is 7C₄ ways

The number of ways committe is selected is 3C₁.7C₄= 105 ways