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

Options

A. 240
B. 244
C. 276
D. 285

Answer

C

Explanation

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`