There are two white balls, three black balls, and four red balls in a box. If at least one black ball is to be included in the draw, how many ways may three balls be chosen from the box?
A. 32
B. 48
C. 64
D. 96
Answer:C
There are two white balls, three black balls, and four red balls in a box. If at least one black ball is to be included in the draw, how many ways may three balls be chosen from the box?
A. 32 B. 48 C. 64 D. 96
Explanation: We may have (1 black and 2 non-black) or (2 black and 1 non-black) or (3 black and 1 non-black) (3 black).3 x 6 x 5/2 x 1 + 3 x 2/2 x 1 x 6 + 1 = (3C1 x 6C2) + (3C2 x 6C1) + (3C3) = 3 x 6 x 5/2 x 1 + 3 x 2/2 x 1 x 6 + 1,(45 + 18 + 1) equals 64.