In a family, 5 males and 3 females are there. In how many ways we can select a group of 2 males and 2 females from the family?(a) 3(b) 10(c) 30(d) 40The question was asked by my college director while I was bunking the class.My query is from Combinations in chapter Permutations and Combinations of Mathematics – Class 11

In a family, 5 males and 3 females are there. In how many ways we can

1.	In a family, 5 males and 3 females are there. In how many ways we can select a group of 2 males and 2 females from the family?(a) 3(b) 10(c) 30(d) 40The question was asked by my college director while I was bunking the class.My query is from Combinations in chapter Permutations and Combinations of Mathematics – Class 11
Answer» Right choice is (c) 30 Best explanation: Out of 5 males, 2 males can be selected in ^5C2 ways. ^5C2 = \(\frac{5!}{(5-2)! 2!} = \frac{543!}{(3)! 2!} = \frac{20}{2}\) = 10 ways. Out of 3 females, 2 females can be selected in ^3C2 ways . ^3C2 = \(\frac{3!}{(3-2)! 2!} = \frac{32!}{(1)! 2!} = \frac{3}{1}\) = 3 ways. So, by the FUNDAMENTAL principle of counting we can SELECT a GROUP of 2 males and 2 females from the family in 103 = 30 ways.

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