Question

The number of 5 digit numbers can be made from the digits 0,1,2,3,4,5 if repetition is not allowed is _____

Answer 1

Observing the given digits 0,1,2,3,4,5 we can see that 0 must not present in the leftmost digit a number to be a 5 digit number.

So, the leftmost digit can be filled with either of the digits 1 or 2 or 3 or 4 or 5, which can be done in 5 ways.

The next digit can be filled with the 5 remaining digits including 0 (exclude digit filled in leftmost place and include 0) which can be done in 5 ways again.

Proceeding in this way, the next digits can be filled in 4 , 3 , 2 ways respectively as shown below.

So, the total number of possible 5 digit numbers = $5\times 5\times 4\times 3\times 2$ = 600