If there are 6 alike fruits,7 alike vegetable | vedclass

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Question

(B) Since the items in each category are alike,the number of ways to select items from each category is equal to the number of items available plus on

Vedclass · Accepted Answer

$336$

Vedclass · Answer

(B) Since the items in each category are alike,the number of ways to select items from each category is equal to the number of items available plus one (for the case of selecting zero items).For $6$ alike fruits,the number of ways to select is $(6+1) = 7$.For $7$ alike vegetables,the number of ways to select is $(7+1) = 8$.For $8$ alike biscuits,the number of ways to select is $(8+1) = 9$.To ensure at least one item from each category is selected,we must select at least $1$ fruit,$1$ vegetable,and $1$ biscuit.The number of ways to select at least one fruit is $6$.The number of ways to select at least one vegetable is $7$.The number of ways to select at least one biscuit is $8$.Therefore,the total number of ways is $6 	imes 7 	imes 8 = 336$.

If there are $6$ alike fruits,$7$ alike vegetables,and $8$ alike biscuits,then the number of ways of selecting any number of things out of them such that at least one from each category is selected,is

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