Aptitude Day 124

Problems on Permutations and Combinations:

1. From a group of 4 men and 2 women, 3 persons are to be selected to form a committee so that at least 2 men are there on the committee. In how many ways can it be done?

Solution:
               =  ⁴C2 *  ²C1 + ⁴C3
               =  ⁴C2 *  ²C1 + ⁴C1
               =  (4*3)/(1*2) * 2 +
               = 12 +4
               = 16.

2. From a group of 6 boys and 3 girls, 5 children are to be selected. In how many different ways can they be selected such that at least 3 boys should be there?

Solution:
               = ( ⁶C3 * ³C2) + ( ⁶C4 *  ³C1 ) +( ⁶C5 )
               = [(6*5*4)/(1*2*3) * ³C1] +[ ⁶C2 * 3 ] + ⁶C1
               = [20*3] +[(6*5/1*2)*3] +6
               = 60+45+6
               = 111.