Form an even number

Probability Level pending

A number of five different digits is formed at random from the digits ( 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 ) (1,2,3,4,5,6,7,8,9) . 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 3 3 decimal places.


The answer is 0.444.

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1 solution

The fundamental experiment is the forming of a number of five different digits . The number of ways of doing this is 9 P 5 = 15120 9P5=15120 .

The number of ways in which we can form an even number of five different digits is 8 × 7 × 6 × 5 × 4 = 6720 8\times 7 \times 6\times 5\times 4=6720 .

Therefore, the desired probability is 6720 15120 = \dfrac{6720}{15120}= 4 9 = \dfrac{4}{9}= 0.444 \boxed{0.444}

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