Discrete Mathematical Structures by Pearson

Combinatorics 5-37

= 1 - (1- 0.4) (1- 0.3) (1- 0.2) (1- 0.1)

= 1 - 0.6 × 0.7 × 0.8 × 0.9

= 1 - 0.3024

= 0.6976

Example 12 A five-digit number is formed by digits 1, 2, 3, 4, 5 without repetition. Find the

probability that the number is divisible by 4.

Solution: Total number of five-digit numbers = 5! = 120

Now a number is divisible by 4 if the last two digits (i.e., digits at unit and 10 place) are

divisible by 4. Therefore, the last two digits can be 12, 24, 32, 52 and thus there are four ways.

Corresponding to each of these, there are 3! = 6 ways of filling the remaining three digits.

Hence, the total number of favourable ways = 6 × 4 = 24

∴The required ...