A 4 person grievance commitee is to be selected out of 2 departments A and B wit

Question

A 4 person grievance commitee is to be selected out of 2 departments A and B with 15 and 27 people respectively. In how many ways can the following commitees be selected A- 3 from A and 1 from b B- 2 from A and 2 from B C- 4 from A D- 4 people regardless of department E- at least 3 from A A 4 person grievance commitee is to be selected out of 2 departments A and B with 15 and 27 people respectively. In how many ways can the following commitees be selected A- 3 from A and 1 from b B- 2 from A and 2 from B C- 4 from A D- 4 people regardless of department E- at least 3 from A A- 3 from A and 1 from b B- 2 from A and 2 from B C- 4 from A D- 4 people regardless of department E- at least 3 from A

Explanation / Answer

A) 3 people can be chosen from A as 15C3 and

1 person can be chosen from B as 27C1

therefore, no. of ways = (15C3 )(27C1) = 12285

B) 2 people can be chosen from A as 15C2 and

2 people can be chosen from B as 27C2

therefore, no. of ways = (15C2 )(27C2) = 36855

C) All 4 people can be chosen from A as 15C4 and

therefore, no. of ways = 15C4= 1365

D) Total no. of people = 15 + 27 = 42

4 people can be chosen regardless of department as 42C4= 111930

E)Atleast 3 from A means

(15C3 )(27C1) +  (15C4 ) = 12285 + 1365 = 13650

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