If `lamda` be the number of 3-digit numbers are of the form xyz with `x lt y, z le y and x ne0`, the value of `(lamda)/(30)` is

Explanation

Since, `x ge1, ` then `x ge 2" "[becausex lty]`
If y=n, then x takes values form 1 to n-1 and z can take the values from 0 to n-1 (i.e., n values)
thus, for each values of `y(2 le y le9), x and z` take `n(n-1)`
vlaues.
Hence, the 3-digit numbers are of the form xyz
`=underset(n=2)overset(9)(sum)n(n-1)=underset(n=1)overset(9)(sum)n(n-1)" "[because" at "n=1,n(n-1)=0]`
`=underset(n=1)overset(9)(sum)n^(2)-underset(n=1)overset(9)(sum)n`
`=(9(9+1)(18+1))/(6)-(9(9+1))/(2)`
`=285-45`
`=240=lamda" "[given]`
`therefore(lamda)/(30)=8`