Question

Lucy Furr must supply 4 different bags of chips for a party. She finds 13 varieties at her local grocer. How many different selections can she make?

Answer 1

Number of selections she can make = 715

Explanation:

Number of bags she must supply = 4

Number of varieties = 13

Number of selections =
`13C4`

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

`13C4 = (13!)/((13-4)!4!) \\13C4 = (13!)/(9!4!) \\13C4 = (13*12*11*10)/(4*3*2*1) \\13C4 = 13 * 11 * 5 \\13C4 = 715`

Number of selections she can make = 715

Answer 2

715

Explanation:

What we must do is apply the concept of combinations, which is the following formula:

nCr = n! / r! * (n - r)!

Where 'n' represents the number of elements available and 'r' represents the number of elements chosen.

In this case, n equals 13 and r equals 4.

replacing in the formula:

13C4 = 13! / 4! * (13 - 4)!

13C4 = 13! / (4! * 9!)

13C4 = 715