Question

Suppose, there are 7 of your friends who want to eat pizza (8 distinct people in total). You order a 16-cut pizza (16 identical slices). How many distributions of pizza slices are there if each person gets at least one slice of pizza?

(a) 346

(b) 6435

(c) 3214

(d) 765

The question was posed to me in quiz.

My question comes from Counting topic in section Counting of Discrete Mathematics

Answer 1

The correct option is (b) 6435

For explanation: This problem can be viewed as identical objects distributed into distinct non-empty bins. Using the formula for these kind of distributions ^n-1Cr-1 = ^15C7 = 6435. Thus, there are distributions of the pizza slices.