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Q.)For a college debating team, 5 gents and 3 lady students were available. It is desired to select 2 gents and 2 ladies to form the team. In how many ways, the team can be selected?

(A) 30

(B) 60

(C) 15

(D) 12

Solution :

2 gents and 2 ladies can be selected in ${ { 5 }_{ C } }_{ 2 }{ { X3 }_{ C } }_{ 2 }$

= $\frac { 5! }{ (5-2)!2! } { { X\frac { 3! }{ (3-2)!2! } } }$

=$\frac { 5! }{ 3!2! } { { X\frac { 3! }{ 1!2! } } }$

= 10 X 3 = 30

Hence Option(A)