Question

There are 16 entrees available at a restaurant. From these, Archie is to choose 6 for his party. How many groups of 6 entrees can he choose, assuming that the order of the entrees chosen does not matter ?

Answer 1

Answer: 8008

Step-by-step explanation:

Total entrees = 16

Number of entrees to choose = 6

Since order does not matter , so we combinations .

Number of combinations to choose r things out of n = $C(n,r)=\dfrac{n!}{r!(n-r)!}$

Then, total ways to choose 6 entrees = $C(16,6)=\dfrac{16!}{6!10!}$

$=\dfrac{16\times15\times14\times13\times12\times11\times10!}{(720)10!}\\\\= 8008$

Hence, the required number of ways= 8008