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(A) The total number of balls in the box is $2 + 3 + 4 = 9$ balls.We need to select $3$ balls such that at least one black ball is included.The number

Vedclass · Accepted Answer

$64$

Vedclass · Answer

(A) The total number of balls in the box is $2 + 3 + 4 = 9$ balls.We need to select $3$ balls such that at least one black ball is included.The number of black balls is $3$ and the number of non-black balls is $2 + 4 = 6$.The selection can be made in the following $3$ mutually exclusive ways:$(i)$ $1$ black ball and $2$ non-black balls: $^3C_1 	imes ^6C_2 = 3 	imes 15 = 45$$(ii)$ $2$ black balls and $1$ non-black ball: $^3C_2 	imes ^6C_1 = 3 	imes 6 = 18$$(iii)$ $3$ black balls and $0$ non-black balls: $^3C_3 = 1$Therefore,the total number of ways = $45 + 18 + 1 = 64$.

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

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