Guest55 wrote:

Surferfish - that is

**wrong** if they aren't distinct.

Please don't give formulae that are totally inappropriate at this level

Hi Guest55.

The 4 digits in the original question were distinct. But you're quite right, in my general definition I should have specifically stated DISTINCT objects for it to be completely correct. Obviously if you have the digits 9, 9, 9, 9 there is only one 4-digit number you can make from them!

I take your point that factorials are beyond what is expected at 11+, but if you forget about the word "factorial" and the "!" symbol then the actual rule is quite simple and easy enough for an 11 year old to remember and use I would think?

Basically if you have a number of DISTINCT things the number of ways you can arrange those things is given by (number of things) * (number of things -1) *(number of things -2) ... down to 1.

Out of interest, what method would you suggest? The only other way I can think of is by trying to write down all the different combinations. This is a good way to understand the problem, but the disadvantage is that it is quite time consuming and these tests tend to be very time pressured.

Are there any other quick and simple ways to get the answer that are more age appropriate?