To develop the mathematics department of a new branch of a s

To develop the mathematics department of a new branch of a state university, the newly elected head of the department must choose two full professors from among six applicants, two associate professors from among ten applicants, and six assistant professors from among sixteen applicants. In how many different ways can she make this choice?

Solution

No . of different ways can she make this choice = 6 C 2 * 10 C 2 * 16 C 6 = [ 6! / 2! * (6-2)! ] * [ 10! / (10-2)! * 2! ] * [ 16! / (16-6)! * 6! ] = 5405400 ways are possible