### Home > CCA2 > Chapter 12 > Lesson 12.2.2 > Problem12-113

12-113.

Andrea has just purchased a five-digit combination lock that allows her to set up her own combination. She can use the numbers $0$ through $9$ for her combination, and she must use five digits.

1. How many five-digit combinations can she make so that no digit is repeated?

Although the problem says 'combination' this is actually a permutation
because the order you enter the numbers in the combination lock matters.

2. How many five-digit combinations are possible if she can repeat the digits, but cannot use the same digit twice in a row?

Since this is a special case you can use a decision chart.
How many choices does she have for each position?

$\frac{ }{1\text{st}}\frac{ }{2\text{nd}}\frac{ }{3\text{rd}}\frac{ }{4\text{th}}\frac{ }{5\text{th}}$

$\frac{10}{1\text{st}} \frac{9}{2\text{nd}} \frac{9}{3\text{rd}} \frac{9}{4\text{th}} \frac{9}{5\text{th}}$