Question

At the grocery store Jack has narrow down his selections to seven vegetables seven fruits four cheeses and four whole-grain breads. He wants to use the express lane so he can only buy 15 items how many ways can he choose which 15 items to buy if he wants all four cheeses?

Answer 1

We know that Jack has narrowed down his selection to a total of:

$7+7+4+4=22$

items.

Since he wants all the cheeses and he wants to use the express lane he needs to select a total of:

$15-4=11$

more items.

From the total number of items he will select:

$22-4=18$

items.

Then he needs to select 11 item from 18 possible items. To determine in how many ways can do this we can use a combination, a combination is given by:

$C(n,r)=\frac{n!}{r!(n-r)!}$

Then we have:

$C(18,11)=\frac{18!}{11!(18-11)!}=31824$

Therefore, there are 31824 ways Jack can choose 15 items if he wants all the cheeses