# A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least one black ball is to be included in the draw ?

A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least one black ball is to be included in the draw ?

A. 32

B. 48

C. 64

D. 96

E. None of these

### **Answer : ** C. 64

## Explanation:

We may have ( 1 black and 2 non-black ) or ( 2 black and 1 non- black ) or ( 3 black ).

Required number of ways = (^{3}C_{1} x ^{6}C_{2}) + (^{3}C_{2} x ^{6}C_{1}) + (^{3}C_{3}) = 64.