A box contains 2 white balls,3 black balls an | vedclass

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(C) Total number of balls $= 2 + 3 + 4 = 9$.Number of black balls $= 3$.Number of non-black balls $= 2 + 4 = 6$.We need to select $3$ balls such that

Vedclass · Accepted Answer

$64$

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(C) Total number of balls $= 2 + 3 + 4 = 9$.Number of black balls $= 3$.Number of non-black balls $= 2 + 4 = 6$.We need to select $3$ balls such that at least one is black.This can be done in the following ways:$1$ black and $2$ non-black balls: ${}^{3}C_{1} 	imes {}^{6}C_{2} = 3 	imes 15 = 45$.$2$ black and $1$ non-black balls: ${}^{3}C_{2} 	imes {}^{6}C_{1} = 3 	imes 6 = 18$.$3$ black and $0$ non-black balls: ${}^{3}C_{3} 	imes {}^{6}C_{0} = 1 	imes 1 = 1$.Total ways $= 45 + 18 + 1 = 64$.

$A$ 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?

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