It is currently Thu Aug 18, 2022 12:25 am

 All times are UTC [ DST ]

 Page 1 of 1 [ 6 posts ]
 Print view Previous topic | Next topic
Author Message
 Post subject: 11+ questionPosted: Sat May 09, 2020 3:30 pm

Joined: Fri Jan 11, 2019 12:57 am
Posts: 63
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

Top

 Post subject: Re: 11+ questionPosted: Sat May 09, 2020 5:46 pm

Joined: Wed May 09, 2007 3:09 pm
Posts: 1289
Location: Solihull, West Midlands
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)

Top

 Post subject: Re: 11+ questionPosted: Mon May 11, 2020 11:27 am

Joined: Fri Mar 10, 2017 5:06 pm
Posts: 682
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.

Top

 Post subject: Re: 11+ questionPosted: Mon May 11, 2020 1:05 pm

Joined: Mon Feb 12, 2007 2:21 pm
Posts: 16254
Surferfish - that is wrong if they aren't distinct.

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

Top

 Post subject: Re: 11+ questionPosted: Tue May 12, 2020 3:46 pm

Joined: Fri Mar 10, 2017 5:06 pm
Posts: 682
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?

Top

 Post subject: Re: 11+ questionPosted: Tue May 12, 2020 5:11 pm

Joined: Mon Jun 18, 2007 3:32 pm
Posts: 7884
Location: East Kent

1234
1243

1324
1342 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

Top

 Display posts from previous: All posts1 day7 days2 weeks1 month3 months6 months1 year Sort by AuthorPost timeSubject AscendingDescending
 Page 1 of 1 [ 6 posts ]

 All times are UTC [ DST ]

#### Who is online

Users browsing this forum: No registered users and 5 guests

 You cannot post new topics in this forumYou cannot reply to topics in this forumYou cannot edit your posts in this forumYou cannot delete your posts in this forumYou cannot post attachments in this forum

Search for:
 Jump to:  Select a forum ------------------ FORUM RULES    Forum Rules and FAQs 11 PLUS SUBJECTS    VERBAL REASONING    MATHS    ENGLISH    NON-VERBAL REASONING    CEM 11 Plus GENERAL    GENERAL 11 PLUS TOPICS    11 PLUS APPEALS    INDEPENDENT SCHOOLS    11 PLUS CDs/SOFTWARE    11 PLUS TIPS    PRIMARY    SEN and the 11 PLUS    EVERYTHING ELSE .... 11 PLUS REGIONS    Berkshire    Bexley and Bromley    Birmingham, Walsall, Wolverhampton and Wrekin    Buckinghamshire    Devon    Dorset    Essex    Essex - Redbridge    Gloucestershire    Hertfordshire (South West)    Hertfordshire (Other and North London)    Kent    Lancashire & Cumbria    Lincolnshire    Medway    Northern Ireland    Surrey (Sutton, Kingston and Wandsworth)    Trafford    Warwickshire    Wiltshire    Wirral    Yorkshire BEYOND 11 PLUS    Beyond 11 Plus - General    GCSEs    6th Form    University