Question

Person A owns three pairs of pants and twelve shirts. In how many ways can this person pack two pairs of pants and four shirts for a weekend trip?

Answer 1

Number of ways to select r items from n, nCr = n!/(r! x (n-r)!)

Number of pants = 3

Number of ways to select 2 pants = 3C2

= 3!/(2! x 1!)

= 3

Number of shirts = 12

Number of ways to select 4 shirts = 12C4

= 12!/(4! x 8!)

= 495

Number of ways to pack two pairs of pants and four shirts for a weekend trip = Number of ways to select 2 pants x Number of ways to select 4 shirts

= 3 x 495

= 1485