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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.

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