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Question
A number of two digits is formed using the digits 1, 2, 3, ….., 9. What is the probability that the number so chosen is even and less than 60?
Solution
The number of two digits can be formed from the given 9 digits in 9 × 9 = 81 different ways.
∴ n(S) = 81
Let A be the event that the number is even and less than 60.
Since the number is even, the unit place of two digits can be filled in 4P1 = 4 different ways by anyone of the digits 2, 4, 6, 8.
Also, the number is less than 60, so tenth place can be filled in 5P1 = 5 different ways by anyone of the digits 1, 2, 3, 4, 5.
∴ n(A) = 4 × 5 = 20
∴ Required probability = P(A) = `("n"("A"))/("n"("S")) = 20/81`
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