The global government of the planet Rentahs functions as a d

The global government of the planet Rentahs functions as a democracy with four major political parties, the Aruhu, the Iekat, the Nahood, and the Yomin. The artifical intelligence committee of the government currently consists of 3 Aruhu, 4 Iekat, 9 Nahood, and 7 Yomin and suppose that a 4-member subcommittee is formed for the purpose of studying human-robot relations.

A. How many different subcommittees are possible?

B. How many different subcommittees consist of at most 1 Iekat?

C. How many different subcommittees consist of exactly 1 Aruhu and at least 2 Yomin?

Solution

Total of all sets = 3+4+9+7 = 23

committe formed have members = 4

A) No of subcommittees = No of ways 4 men can be selected from 23

= 23C4

B) Subcommittes formed of atmost one lekat can be

either 0 lekat or 1 lekat

= (19C4) + 4C1(19C3)

C) Exactly 1 Aruhu and atleast 2 Yomin

= 3C1 {(7C2 13C1)+7C3)