A number of five different digits is formed at random from the digits . Find the probability that it will be an even number. Repetition of any digit is not allowed. Give your answer as a decimal number correct to decimal places.
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The fundamental experiment is the forming of a number of five different digits . The number of ways of doing this is 9 P 5 = 1 5 1 2 0 .
The number of ways in which we can form an even number of five different digits is 8 × 7 × 6 × 5 × 4 = 6 7 2 0 .
Therefore, the desired probability is 1 5 1 2 0 6 7 2 0 = 9 4 = 0 . 4 4 4