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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

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

Similar Questions

$A$ student is allowed to select at least $(n+1)$ books but not all books from a collection of $(2n+1)$ books. If the total number of ways in which he can select these books is $255$,then the number of books in that collection is

There are $15$ persons in a party and each person shakes hands with every other person exactly once. The total number of handshakes is:

If ${ }^{n+4} C_{n+1}-{ }^{n+3} C_n=15(n+2)$,then $n=$

Evaluate $\frac{n!}{r!(n-r)!}$ when $n=5$ and $r=2$.

$A$ student is allowed to choose at most $n$ books from a collection of $2n+1$ books. If the total number of ways in which he can select at least one book is $255$,then the value of $n$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module