Question

How many numbers greater than 2000 can be formed with digits 1,2,3,4,5 ?

Answer 1

Only a four digit number is greater than 2000. So we've to use all four digits.

The problem can be seen in two ways:

Without repetition:

The first digit can't be 1 as number required is greater than 2000. So there are three possibilities 2,3,4. For second digit it can be 1 or remaining two digits. Hence three ways. Similarly third digit can be chosen in two ways and the last one is the one which is left.

Thus number of ways =3×3×2×1=18=3×3×2×1=18

With repetition:

The question is not clear so I'll assume four digit numbers greater than 2000. First digit can't be 1. So there are 3 ways. The rest of three digits can be any of 1,2,3,4.

Thus number of ways =3×4×4×4=192