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

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Question

(B) To form a group,we must select a subset of the available balls.For the $5$ different green balls,the number of ways to select at least one green b

Vedclass · Accepted Answer

$3720$

Vedclass · Answer

(B) To form a group,we must select a subset of the available balls.For the $5$ different green balls,the number of ways to select at least one green ball is $2^5 - 1 = 31$.For the $4$ different blue balls,the number of ways to select at least one blue ball is $2^4 - 1 = 15$.For the $3$ different red balls,we can either select or not select each ball,which gives $2^3 = 8$ ways.Since the selections are independent,the total number of ways to form the group is $31 	imes 15 	imes 8 = 3720$.

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 must be included.

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