There are 11 top managers that need to form a decision

Question

:evil: There are 11 top managers that need to form a decision group. How many ways are there to form a group of 5 if the President and Vice President are not to serve on the same team

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kapslock · Answer

I am assuming that the 11 top managers include the Prez and the VP.

Then, if the Prez is in the team, out of 11 - Prez - VP, 4 selections need to be made = C(9,4) = 126

Similarly, if VP is in the team, out of 11 - Prex - VP, 4 selections need to be made C(9,4) = 126.

And if none of them is in the team, then 5 out of 9 selections need to be made = C(9,5) = 126.

Thus total number of ways = 378.

Jacques · Answer

You rock

You are right that is the OA kapslock but can you strech you mind and think of anyother alternatives of solving.

Srinivas · Answer

Alternately, You can look at this as follows:

Out of a team of 11, 5 can be selected in 11C5 ways

If both P & VP inlcuded in the team, you can select the team in 9C3 ways.

The problem asks for P&VP not serve on the same team.

So, the answer is 11c5 - 9c3 = 378.

-Srinivas

MA · Answer

i would do this way.

Srinivas · Answer

Normally, I would look for multiple ways to tackle a problem. This gives me an opportunity to validate my answer. What I am suggesting does not mean to take credit away from others.

Keep both methods handy. If you are ahead of time, you can check your answer. 

In this problem, numbers are kinda big. If the numbers are small, you might be able to use both methods and still finish the problem in less than a minute.

Thanks though.

-Srinivas.

There are 11 top managers that need to form a decision

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