11 Plus Exams Forum

Hi All,

I’m stumped with this question How many different 4-digit numbers can be made using all four of the digits 1, 2, 3 and 5?

My DD was doing a 8 min test and that question cake up. I’ve never seen anything like it before. Thanks

Take it in stages:

How many choices are there for the first digit?
Then when you've picked that one, how many choices are there for the next digit?
Then there are only two options left for how you arrange the last two digits!

Maybe without the pressure of time try writing them all out - these kinds of questions come up a lot (sometimes "make the biggest number you can out of these digits" or " how close can you get to 4000?" or "how many of the numbers you can make are even?" - all good practice)

The answer is 4! = 4(factorial) = 4 * 3 * 2 * 1 = 24

In general if you have a group of n objects (digits, cards, people, whatever) there are n! different ways of ordering them in a sequence.

Surferfish - that is wrong if they aren't distinct.

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

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?

Start with 1

1234
1243

1324
1342 etc

then start with 2 etc.

and so on.


Check to make sure you haven't repeated any

Encourage child to work systematically, can they see any patterns? Predict anything?

an