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If lamda be the number of 3-digit numbers are o the form xyz with x lt y, z lt y and x ne0, the value of (lamda)/(30) is |
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Answer» Solution :Since, `x ge1, ` then `x ge 2""[becausex LTY]` If y=n, then x takes values form 1 to n-1 and zcan 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` |
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