Chapter 12.6, Problem 30P

There are 15 slips of paper in a jar. Each slip has a different name on it. How many ways can you draw 5 names from the jar?

To determine

Find the number of ways that you can draw 5 names from the jar.

Answer to Problem 30P

3003

Explanation of Solution

Given:

There are 15 slips of paper in a jar.Each slip has a different name on it.

Formula Used:

  $C{}_r=\frac{n!}{r!(n-r)!}$

Calculation:

We need to draw 5 slips of paper from 15 slips , without replacement and order does not matter , so, the number of ways that we can draw 5 names from the jar :

  $C{}_5=\frac{15!}{5!(15-5)!}=\frac{15!}{5!10!}=\frac{15\cdot 14\cdot 13\cdot 12\cdot 11\cdot 10!}{5!10!}=3003$ .