## Problem 2

**Problem – 2**

How many strings of five decimal digits

**a)** do not contain the same digit twice?

**b)** end with an even digit?

**c)** have exactly four digits that are 9s?

**Solution:**

a) We have 10 digits to fill 5 places.

We can fill first place with 10 digits and second one with only 9 as repetition is not allowed and so on.

So number of strings of five decimal digits = 10x9x8x7x6 = 30240

b) A number will be even if its last digit is 0,2,4,6,8

So we can fill last place of the string with 5 digits, and rest will 10 digits as repetition is allowed.

So number of strings = 10x10x10x10x5 = 50000

c) When first digit is different than number of possible strings = 9

When second digit is different than number of strings = 9

Same for 3^{rd}, 4^{th} and 5^{th} place,

So total number of strings = 9+9+9+9+9 = 45