List of top Mathematics Questions on Discrete Mathematics asked in IIT JAM MA

There are four different types of bananas. In how many ways can 12 children select bananas so that at least one banana is selected from each type?

There are four different types of bananas. In how many ways can 12 children select bananas so that at least one child selects different types of bananas?

Evaluate: \[ {}^{5}C_{0} + {}^{6}C_{1} + {}^{7}C_{2} + {}^{8}C_{3} + {}^{9}C_{4} + {}^{10}C_{5} + {}^{11}C_{6}. \]