The number of groups that can be made from 5 | vedclass

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(B) To form a group,we must select at least one green ball,at least one blue ball,and any number of red balls (including zero).$1$. Number of ways to

Vedclass · Accepted Answer

$3720$

Vedclass · Answer

(B) To form a group,we must select at least one green ball,at least one blue ball,and any number of red balls (including zero).$1$. Number of ways to select at least one green ball from $5$ different green balls is $2^5 - 1 = 32 - 1 = 31$ ways.$2$. Number of ways to select at least one blue ball from $4$ different blue balls is $2^4 - 1 = 16 - 1 = 15$ ways.$3$. Number of ways to select any number of red balls from $3$ different red balls (including the case of selecting zero red balls) is $2^3 = 8$ ways.Total number of ways = $31 	imes 15 	imes 8 = 3720$.

The number of groups that can be made from $5$ different green balls,$4$ different blue balls,and $3$ different red balls,if at least $1$ green and $1$ blue ball is to be included.

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