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The number of three digit numbers of the...

The number of three digit numbers of the form xyz where x>y >z is

Text Solution

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There can be two cases.
Case 1: When `0` is any of the numbers.
In this case, `z` will be `0`. So, number of ways to select `x` and `y` will be `C(9,2)`.
Case 2: When `0` is not included in any of the numbers.
Number of ways to select `x`,`y` and `z` will be `C(9,3)`.
`:.` Total number of three digits number `= C(9,2)+C(9,3) = 36+84 = 120`
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