there are 9 men's and 4 women in a group of teachers 6 persons are to be selected to form a team so that atleast 4 men's are there in a team in how many ways can it be done
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From a group of 8 men and 4 women, 4 persons are to be selected to form a committee so that at least 2 women are there on the committee. In how many ways can it be done?
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Solution
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Correct option is
A
201
Total number of men =8
Total number of women =4
Committee = 4 persons → at least 2 women
Case 1→2 women + 2 men ⇒
4
C
2
×
8
C
2
=168
Case 2→3 women + 1 men ⇒
4
C
3
×
8
C
1
=32
Case 3→ 4 women + 0 men ⇒
4
C
4
=1
Total
201
∴ There are 201 ways
Given : 9 men's and 4 women in a group of teachers
6 persons are to be selected to form a team so that atleast 4 men's are there in a team
To Find : Number of Ways
Solution:
Mens = 9 , Women = 4
Atleast 4 Men , then 3 possible case
4 Men 2 women , 5 Men 1 Woman , 6 Mens 0 woman
4 Men 2 women can be selected in ⁹C₄.⁴C₂
= 126 * 6
= 756
5 Men 1 women can be selected in ⁹C₅.⁴C₁
= 126 * 4
= 504
6 Men 0 women can be selected in ⁹C₆.⁴C₀
=84 * 1
= 84
Total Ways = 756 + 504 + 84 = 1344
Number of Ways = 1344
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