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(D) The number of ways to select balls from $n_1$ identical items of type $1$,$n_2$ identical items of type $2$,and $n_3$ identical items of type $3$

Vedclass · Accepted Answer

$879$

Vedclass · Answer

(D) The number of ways to select balls from $n_1$ identical items of type $1$,$n_2$ identical items of type $2$,and $n_3$ identical items of type $3$ is given by $(n_1 + 1)(n_2 + 1)(n_3 + 1)$.Here,$n_1 = 10$ (white),$n_2 = 9$ (green),and $n_3 = 7$ (black).Total ways including the case where no ball is selected $= (10 + 1) 	imes (9 + 1) 	imes (7 + 1) = 11 	imes 10 	imes 8 = 880$.Since we need to select one or more balls,we exclude the case where no ball is selected (i.e.,subtract $1$).Number of ways $= 880 - 1 = 879$.

Assuming the balls to be identical except for their color,the number of ways in which one or more balls can be selected from $10$ white,$9$ green,and $7$ black balls is:

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