committee of four is to be chosen from a grout 5 men and 3 women in how many ways can this be done if the chairman must be a man in the community please show workings?

Smashing

6 years ago

The chairman must be a man, and there are 5 ways to select him. After that there will be three more positions to filled from the remaining 7 people, which can be done in 7C3 = 7!/4!3! = 35 ways. The answer is 5 x 35 = 175.

VPETERS2002

6 years ago

First select the most-restrictive position (the Chairman) from among the 5 men; there are 5 ways to do this.
That leaves 7 people (4 men and 3 women) among whom 4 more must be selected (in any combination). Let me count the ways:
7!/(!*(7 )!)=(7*6*5)/(3*2*1)
I guess you can figure out the rest of the computation.
Don’t forget to multiply this by 5.