Question

How many groups of 6 entrees can Archie choose from the 16 available at a restaurant, assuming the order does not matter?

a) 16
b) 32
c) 40
d) 80

Answer 1

Archie can choose from 8,008 different groups of 6 entrees from 16 available, calculated using the combination formula.

Step-by-step explanation:

How many groups of 6 entrees Archie can choose from the 16 available at a restaurant, assuming the order does not matter. This is a problem of combinatorics and can be solved using the combination formula which is given by:

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

where 'n' is the total number of items to choose from, 'k' is the number of items to choose, 'n!' is the factorial of 'n', 'k!' is the factorial of 'k', and '(n - k)!' is the factorial of the difference between 'n' and 'k'.

In this case, n = 16 and k = 6, so the calculation would be:

C(16, 6) = 16! / (6! * (16 - 6)!)
= 16! / (6! * 10!)
= (16 * 15 * 14 * 13 * 12 * 11) / (6 * 5 * 4 * 3 * 2 * 1)
= 8,008

Therefore, Archie can choose from 8,008 different groups of 6 entrees.