A committee of three is to be formed from five math teachers

[kimmy_koo51]

A committee of three is to be formed from five math teachers and four English teachers. In how many ways can the committee be formed if order matters and there must be at least one mathematics teacher?

 

[Tuugii]

Hello Kimmy,

I guess its: C(5,1)xC(4,2) = 5x(P(4,2)/P(2,2)) = 5x(4x3/2x1) = 30.

Tuugii

 

[galactus]

Since order matters, there are P(9,3) ways to select 3 without restriction.

The opposite of at 'least one' math teacher is no math teachers.

There are P(4,3) ways.

Therefore, P(9,3)-P(4,3)