Question

The number of numbers lying between 100 and 1000 can be formed with the digits 1,2,3,4,5,6,7is

Answer 1

The numbers range from 101 to 999 are 3 digit numbers.  There is no restriction. Any digit can appear any number of times.

So ways of selecting 3 digits out of 7 digits :  7*7*7 = 343

Answer 2

Allowed digits are, 1, 2, 3, 4, 5, 6, 7
[Total Digit Count (n) = 7]

Now we have to form three digit numbers using given 7 digits.

(H)__,(T)__,(U)__

Now Hundred's place can be filled by any of 7 digits as well as, Ten's and Unit's place, so we have total 7*7*7 = 343 numbers.

Answer
343