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A five digit number if formed by the digits 1,2,3,4,5,6 and 8. The probability that the number has even digit at both ends is

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A five digit number if formed by the digits 1,2,3,4,5,6 and 8. The probability that the number has even digit at both ends is A. 3 7 B. 4 7 C. 2 7 D. none of these Select the correct answer from above options

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Correct Answer - C Total number of 5 digit numbers formed with the given digits =.7C5×5! There are 4 even digits out of which two even digits (for both ends) can be chosen in .4C2 ways. Therefore, the two ends can be filled in 2×.4C2 ways. Now, remaining three places can be filled in .5C3×3! ways. ∴ Number of 5 digit, numbers having even digits at both ends =2×.4C2×.5C3×3! Required probability = 2×.4C2×.5C3×3! .7C5×5! = 2 7

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