Question

From 5 gentelmen and 5 ladies, a committee of 4 members
is to be formed. In how may ways can be committee be
formed, so that each comittiee shall contain at least one
gentlemen and one lady.
Answer fast the correct one will get 100 points​

Answer 1

Answer:

(a) There should atleast be one lady, i.e., (L,G)≡(1,4),(2,3),(3,2),(4,1)

So, we will choose L ladies from 4 and G gentlemen from 6,

=

1

4

C.

4

6

C+

2

4

C.

3

6

C+

3

4

C.

2

6

C+

4

4

C.

1

6

C=60+120+60+6=246

(b)There is no restrictions

=

5

10

C=252

Answer 2

If at least one woman has to be included then the committee can be formed as:

• 1 woman and 2 men

• 2 women and 1 man

∴ Number of ways of forming the committee = 2C1 × 5C2 + 2C2 × 5C1

= 2 × 10 + 1 × 5

= 20 + 5

= 25.