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There are 7 women and 5 men in a department.
a) how many ways can a committee of 3 people be selected?
b) how many ways can a committee of 2 men and 1 woman be selected?
c) how many ways can a committee of at least 2 woman be selected (3 people total)?

Correct answer:

a =  220
b =  70
c =  140

Step-by-step explanation:

w=7 m=5 t=w+m=7+5=12  a=3!t (t1) (t2)=3!12 (121) (122)=220
b=m (m1)/2 w=5 (51)/2 7=70
C2(7)=(27)=2!(72)!7!=2176=21 C3(7)=(37)=3!(73)!7!=321765=35 c=(2w) m+(3w)=21 5+35=140

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