From A Group Of 7 Men And 6 Women, Five Persons Are To Be Selected To

1.	From A Group Of 7 Men And 6 Women, Five Persons Are To Be Selected To Form A Committee So That At Least 3 Men Are There In The Committee. In How Many Ways Can It Be Done?
Answer» From a group of 7 men and 6 women, five persons are to be selected with at least 3 men. Hence we have the following 3 options. We can select 5 men à Number of ways to do this = 7C5 II) We can select 4 men and 1 woman à Number of ways to do this = 7C4 × 6C1 iii) We can select 3 men and 2 women à Number of ways to do this = 7C3 × 6C2 Total number of ways = 7C5+ (7C4 × 6C1) + (7C3× 6C2) = 7C2+ (7C3× 6C1) + (7C3×6C2) —- Expand this using nCr = nC (n – r) = 21 + 210 + 525 = 756. From a group of 7 men and 6 women, five persons are to be selected with at least 3 men. Hence we have the following 3 options. We can select 5 men à Number of ways to do this = 7C5 ii) We can select 4 men and 1 woman à Number of ways to do this = 7C4 × 6C1 iii) We can select 3 men and 2 women à Number of ways to do this = 7C3 × 6C2 Total number of ways = 7C5+ (7C4 × 6C1) + (7C3× 6C2) = 7C2+ (7C3× 6C1) + (7C3×6C2) —- Expand this using nCr = nC (n – r) = 21 + 210 + 525 = 756.

From A Group Of 7 Men And 6 Women, Five Persons Are To Be Selected To Form A Committee So That At Least 3 Men Are There In The Committee. In How Many Ways Can It Be Done?

Answer»

From a group of 7 men and 6 women, five persons are to be selected with at least 3 men.

Hence we have the following 3 options.

We can select 5 men à Number of ways to do this = 7C5

II) We can select 4 men and 1 woman à Number of ways to do this = 7C4 × 6C1

iii) We can select 3 men and 2 women à Number of ways to do this = 7C3 × 6C2

Total number of ways = 7C5+ (7C4 × 6C1) + (7C3× 6C2)

= 7C2+ (7C3× 6C1) + (7C3×6C2) —- Expand this using nCr = nC (n – r)

= 21 + 210 + 525 = 756.