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Question

# How many numbers greater than 56000 can be formed by using the digit 4,5,6,7,8 with no digit repeated.

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Solution

## To form numbers greater than 56000 using the digits 4,5,6,7,8 without repetition can be done (1)Taking first digit as 5 OR (2) first digit greater than 5 (1) If the first digit is 5 can be done in 1 way The second digit without repetition can be done in 3 ways ( it can not be 4) Rest of the 3 digits can be done in 3! = 6 ways Therefore Taking first digit as 5 numbers greater than 56000 can be formed =1x3x6=18 OR (2) First digit is greater than 5 The first digit can be formed in 3 ways. Rest of the 4 digits can be done in 4!=24 Therefore Taking first digit > 5 numbers greater than 56000 can be formed = 3 x 24 = 72 Hence Numbers greater than 56000, using the digits 4,5,6,7,8 without repeating=18+72=90

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