a committee consisting of 5 members is to be formed selected out of 6 men and 4 women.

Question

Ђơ̴̴̴̴̴̴͡ω​ many commitees can be formed,so that at least one woman is always there in the committee

Answer 1

the committee format will be MMMMM,WMMMM,WWMMM, WWWMM, WWWWM

method one: all the possible committee  : 10C5

                   the committee with only Men  : 6C5

                 thus the require committee will be 10C5 - 6C5 = 246

 

method two :  committee with one Woman = 4C1 x 6C4 = 60

                     committee with two Women = 4C2 x  6C3 =120

                     committee with three Women = 4C3 x 6C2 = 60

                     committee with four  Women = 4C4 x 6C1= 6

                     total number of committees = 60+120+60 + 6 = 246