Probability of a committee of 3?

Question

8 Democrats, 7 Republicans, 5 Independents.

Probability of a committee that has:

2 Democrats and 1 Republican?

3 Independents?

no Independents?

1 Democrat, 1 Repub., 1 Independ.?

Answer 1

a. (8 taken 2)(7 taken 1)/(20 taken 3)

b. (5 taken 3)/(20 taken 3)

c. {(8 taken 3)+(8 taken 2)(7 taken 1)+(8 taken 1)(7 taken 2)+ (7    

               taken 3)}/(20 taken 3)

d. (8 taken 1)(7 taken 1)(5 taken 1)/(20 taken 3)

Answer 2

2D&1R -

3 x 8/20 x 7/19 x 7/18 = 0.172

3I -

5/20 x 4/19 x 3/18 = 0.009

No I -

15/20 x 14/19 x 13/18 = 0.092

1D, 1R & 1I

6 x 8/20 x 7/19 x 5/18 = 0.246