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? (If necessary, consult a list of formulas.)

a) 240
b) 360
c) 480
d) 720

Answer 1

Archie can choose 8008 groups of 6 entrees from the 16 available.

Step-by-step explanation:

To find the number of groups of 6 entrees that Archie can choose, we can use the combination formula. The combination formula is given by the formula:

C(n, k) = n! / ((n-k)! * k!)

where n is the total number of items, and k is the number of items in each group.

In this case, n = 16 (number of entrees) and k = 6. Plugging these values into the formula:

C(16, 6) = 16! / ((16-6)! * 6!)

Calculating this expression:

C(16, 6) = 16! / (10! * 6!)

Using a calculator or mathematical software, the result is:

C(16, 6) = 8008

Therefore, Archie can choose 8008 groups of 6 entrees from the 16 available.