Question

1. From a group of 6 men and 8 women, a committee consisting of 3 men and 3 women is to be formed. How many different committees can be form if (a) all the men and women are willing to serve; (2 marks) = 1120 (2 marks) (b) l of the men must serve; Cox C8 - 336 (c) 2 of the women refuse to serve together, (3 marks) (d) 1 man and 1 woman refuse to serve together? (3 marks)

I think that my and in b is wrong as well…

Answer 1

a) Number of ways of forming committee here is computed as:
= Number of ways to select 3 men from the 6 men * Number of ways to select 3 women from the 8 women

= (C)(3) 20156 1120 = 20 + 56 = 1120

Therefore there are 1120 ways to select the committee here.

b) Given that one of the men must serve, the number of ways here is computed as:
= Number of ways to select 2 men from the remaining 5 men * Number of ways to select 3 women from the 8 women

ا = 10 * 56 = 560 پن

Therefore there are 560 ways to select the committee here.

c) Given that 2 of the women dont want to work together, number of ways to choose the committee here is computed as:

= Number of ways to select 3 men from the 6 men * (Number of ways to choose 3 women from the 6 remaining women + Number of ways to choose 2 women from the remaining 6 women * Number of ways to choose 1 woman from those 2 women who dont want to work together)

= (3) () + (9) (༣))

= 20120 + 15 * 2] = 1000

Therefore there are 1000 ways to choose the committee here.

d) Given that 1 man and 1 woman refuse to serve together, number of ways to choose the committee here is computed as:

= Number of ways to choose 3 men from remaining 5 men * Number of ways to choose 3 women from the remaining 7 women + Number of ways to choose 3 men from the remaining 5 men * Number of ways to choose 2 women from the remaining 7 women + Number of ways to choose 2 men from the remaining 5 men * Number of ways to choose 3 women from the remaining 7 women

- (1) () + () () + 0)

= 10*35+10+ 21 + 10 +35=910

Therefore there are 910 ways to choose the committee here.