the number of positive integers less than 1,00,000 which contain exactly one 2, one 5 and one 7 in decimal representation is

There are 3 ways of permuting the digits 2,5,7

For each permutation there are 5 places to put it the first digit and 4 places to put it the second digit.

There are 7-7 choices for what the other digits should be.

You are guaranteed that all five digits are distinct, so you don't have to worry about double-counting.

so N=3×4×5×7×7= 2940