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The number of three digit numbers of the...

The number of three digit numbers of the form xyz such that `x lt y , z le y and x ne0`, is

A

240

B

244

C

276

D

285

Text Solution

Verified by Experts

The correct Answer is:
C
In y=n, then x takes values from 1 to n-1 and z can take values from 0 to n(i.e., (n+1)values). Thus, for each values of `y(2leyle9)`, x and z take (n-1)(n+1)values.
Hence, the 3-digit numbers are of the form xyz ltBrgt `=underset(x=2)overset(9)(sum)(n-1)(n+1)=underset(x=2)overset(9)(sum)(n^(2)-1)=276`
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