Question

8. Suppose 7 female and 5 male applicants have been successfully screened for 4
positions. In how many ways can the following compositions be selected?
(i) 2 female and 2 males (ii) 3 females and 1 male (iii) 4 females
(iv) 4 people regardless of sex (v) At least 3 females​

Answer 1

(i) 2 males out of 5 = 5C2 = 10

2 females out of 7 = 7C2 = 21

Total ways = 10 × 21 = 210

(ii) 3 females out of 7 = 7C3 = 35

1 male out of 5 = 5C1 = 5

Total ways = 35 × 5 = 175

(iii) 4 females out of 7 = 7C4 = 35

No males

Total ways = 35

(iv) Total people both men and women = 12

4 people out of 12 = 12C4 = 495

(v) Atleat 3 females

There are two cases

Case A

3 females and 1 male

3 females out of 7 = 7C3 = 35

1 male out of 5 = 5C1 = 5

Way A = 35 × 5 = 175

Case B

All 4 females , No males

4 females out of 7 = 7C4 = 35

Way B = 35

Total ways = way A + way B = 175 +35 = 210

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