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  4. The figures 4, 5, 6, 7, 8 are written in every possible order. The number of numbers greater than 56000 is

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Q. The figures $4, 5, 6, 7, 8$ are written in every possible order. The number of numbers greater than $56000$ is

Permutations and Combinations

Solution:

Reqd. no. of ways $=5\,!-4\,!-3\,!$
[$\because$ number will be less than $56000$ only if either $4$ occurs on the first place or $5$, $4$ occurs on the first two places]
$= 120 - 24 - 6 = 90$