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
Answers
Answered by
9
(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
Hope this helps
All The Best
Mark me BRAINLIEST
Similar questions