In how many ways can a committee of four gentlemen and three ladies be formed out of seven gentlemen and six ladies ?

Explanation

A committee of 4 gentlemen and 3 ladies is to be formed out 7 gentlemen and 6 ladies. `:.` "The number of ways in which the committee can be formed". ""^7C_4xx""^6C_3=(7*6*5)/(3*2)xx(6*5*4)/(3*2)=700`