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

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)=(n!)/(r!(n-r)!)`

Then, total ways to choose 6 entrees =
`C(16,6)=(16!)/(6!10!)`

`=(16*15*14*13*12*11*10!)/((720)10!)\\\\= 8008`

Hence, the required number of ways= 8008