# SOLUTION: A committee of 4 has to be selected from amongst 5 men and 4 women. In how many ways can this be done so as to include at least 1 man and 1 woman.

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 Click here to see ALL problems on Probability-and-statistics Question 388802: A committee of 4 has to be selected from amongst 5 men and 4 women. In how many ways can this be done so as to include at least 1 man and 1 woman. Found 2 solutions by Jk22, robertb:Answer by Jk22(389)   (Show Source): You can put this solution on YOUR website!Choosing 1 man and 1 woman gives 5*4 possibilities, remain to choose 2 people out of 4+3=7 : 7*6 Since the order does not influence, this makes : 5*4*7*6/4! = 5*4*7*6/(4*3*2) = 35 possibilities Answer by robertb(4012)   (Show Source): You can put this solution on YOUR website!# ways of choosing 1 man from 5 = 5C1 = 5. # ways of choosing 1 woman from 4 = 4C1 = 4. # ways of choosing 2 people from 7 remaining people = 7C2 = 21. By the fundamental principle of counting, the #ways of choosing 4 people so as to include at least 1 man and 1 woman is 5*4*21 = 420.