Question

At the grocery store, Hosea has narrowed down his selections to 7 vegetables, 6 fruits, 5 cheeses, and 6 whole grain breads. He wants to use the Express Lane, so he can only buy 15 items. In how many ways can he choose which 15 items to buy if he wants all 5 cheeses?

Answer 1

Answer: 92378

Step-by-step explanation:

Given : At the grocery store, Hosea has narrowed down his selections to 7 vegetables, 6 fruits, 5 cheeses, and 6 whole grain breads.

Total items : 7+6+5+6=24

If he wants all cheeses  , then the remaining items needed to be select = 15-5=10

Total items left from which he will select = 24-5=19

No. of combinations of r things out of n : $C(n;r)=\dfrac{n!}{r!(n-r)!}$

The combination of 10 things selecting from 19 things given by :-

$C(5;5)\timesC(19;10)=\dfrac{19!}{10!(19-10)!}\\\\=(1)\times\dfrac{19\times18\times17\times16\times15\times14\times13\times12\times11\times10!}{10!9!}\ \because ^nC_n=1\\\\=92378$

Hence, the number of ways he can choose 15 items to buy if he wants all 5 cheeses =92378