Statistics and Maple: Constructing a Team of 4 from 3 Groups"

[Mathman2013]

Homework Statement

We have three groups, group 1 contains 21 people, group two contains 18 people and group 3 contain 50 people.

First we need to construct a team of 4 people of three groups.

How many ways can such a team be constructed?

I use combinate such that it will be calculated in Maple.

numbcomb(21+18+50, 4) is number of ways this group can constructed.


second question is tricky one.

How many ways can the group of 4 be constructed if its a requirement that there must be at least one person from each group in the group of 4 ?

The Attempt at a Solution

I know its numbcomb(21+18+50,4) to be used to again. But I am not sure howto proceed.

So any hints of help would be apriacated.

 

[Ray Vickson]

Homework Statement

We have three groups, group 1 contains 21 people, group two contains 18 people and group 3 contain 50 people.

First we need to construct a team of 4 people of three groups.

How many ways can such a team be constructed?

I use combinate such that it will be calculated in Maple.

numbcomb(21+18+50, 4) is number of ways this group can constructed.second question is tricky one.

How many ways can the group of 4 be constructed if its a requirement that there must be at least one person from each group in the group of 4 ?

The Attempt at a Solution

I know its numbcomb(21+18+50,4) to be used to again. But I am not sure howto proceed.

So any hints of help would be apriacated.

Using numbcomb(89,4) again would be a mistake, unless you were willing to perform the very laborious process of then subtracting out the "illegitimate" combinations.

Much easier: first make sure you choose 1 person from each group, giving you a partial group of 3 people. Then you need to choose 1 more person.