Question

How many 5 digit numbers can be made with 1,0,2,4,7 when they can be repeated?

a)25
b)24
c)2500
d)74
e)96

Answer 1

2500

Explanation:

We have five numbers that can be repeated. How many 5-digit numbers can we make?

If the 0 was any other single digit number not already in the list, say 8, we'd be able to say that that number could be found by saying that for each numerical position, there are 5 choices, and so we'd have:

`5^5=3125`

And so what we need to do is set a number that is not 0 in the first position (4 choices) and then allow the other digits be whatever they want to be (4 spots with 5 choices each). And so we end up with:

`4xx5^4=4xx625=2500`