In a group there are 5 men and a certain number of women.From this group, 6 persons including at least 4 men are being sent for a tour evry week. different group is being sent for each week. during the trip each woman is presented with a book. If the totalnumber of books distributed is 156, then find the number of women in the group.

Answer is 6

lets suppose total no of woman =x.

then as total 6 people are selected for a trip and atleast 4 men are to be selected then only two cases are possible.

case 1-

all 5 men included and one woman included.
this can be done in (5c5) X (xc1) different ways
so total books given = xc1=x

case -2

4 men and two woman included.

this can be done in (5c4) X (xc2) ways.
as total woman are 2 so no of books given =2(5c4)(xc2)=5(x)(x-1)

total books given = x + 5(x)(x-1)=156

on solving we get x=6.