Help with maths, I think

[duncandisorderly]

I have 13 different things.
I can only choose 4 things.
I must choose 4 things.

How many combinations of things are there?

[No Ney Never]

Combinations of what; how many there are? how many you can choose? how many you must choose? or a combination of of all?

[Pickles]

Are they free and can they fit in the boot?

[Zero]

715

[duncandisorderly]

Combinations of what; how many there are? how many you can choose? how many you must choose? or a combination of of all?

Erm;
How many are there?
exactly 13

How many must you choose?
exactly 4

[No Ney Never]

Erm;
How many are there?
exactly 13

How many must you choose?
exactly 4

Hardly a puzzle is it?

[Leisure]

17160 combinations

[duncandisorderly]

Hardly a puzzle is it?

No need to be mean just because I can't work it out.

You have A, B, C, D, E, F, G, H, I, J, K, L and M.

You can have any combination of four.

How many combinations are there?

[Leisure]

No need to be mean just because I can't work it out.

You have A, B, C, D, E, F, G, H, I, J, K, L and M.

You can have any combination of four.

How many combinations are there?

17160

[No Ney Never]

No need to be mean just because I can't work it out.

You have A, B, C, D, E, F, G, H, I, J, K, L and M.

You can have any combination of four.

How many combinations are there?

It's already been answered: 715

[yTib]

only one.

[Foreverly Claret]

715

[timshorts]

Yes. You've got two different answers, because you didn't define the question properly.

The large number is the total number of combinations assuming that the order is important like the code for an entry to a keysafe where you can have #,* and + as well as numbers to pick from.
The small number assumes that you have 4 items like cakes in your hand, and it doesn't matter in which order they turned up cos you will put on the calories whatever.

[dougcollins]

You didn't say if the four chosen ones go back into the pool, or are permanently removed.

[Tricky Trevor]

1.2.3.4
1.2.3.5
1.2.3.6
1.2.3.7
Oh! Feck it.

[ClaretTony]

Easy

If it’s a combination, the answer is

13! divided by 4!x9!

[Jasper64]

No need to be mean just because I can't work it out.

You have A, B, C, D, E, F, G, H, I, J, K, L and M.

You can have any combination of four.

How many combinations are there?

I agree with Leisure it's 17160 various combinations.

13x12x11x10=17160

[ClaretTony]

I agree with Leisure it's 17160 various combinations.

13x12x11x10=17160

I’d stick with the 715, the 17,160 is correct if the four selections have to be in the correct order.

So if any order and you select 1-2-3-4 then it is 715 but if you then have 1-2-4-3 etc as extra options then it is 715 x 24 =17,160.

So 715 for combination but 17,160 for permutations.

[Dazzler]

1023

[LeadBelly]

I’d stick with the 715, the 17,160 is correct if the four selections have to be in the correct order.

So if any order and you select 1-2-3-4 then it is 715 but if you then have 1-2-4-3 etc as extra options then it is 715 x 24 =17,160.

So 715 for combination but 17,160 for permutations.

Agree with this.
Non-maths people tend to think that permutations and combinations mean the same but they dont - as per CT's explanation.

I remember doing the pools (pre lottery) and you had "perm 8 from 12" type bets but they were really combinations.

[ClaretTony]

Agree with this.
Non-maths people tend to think that permutations and combinations mean the same but they dont - as per CT's explanation.

I remember doing the pools (pre lottery) and you had "perm 8 from 12" type bets but they were really combinations.

That’s always been a confusion. Pools companies always referred to them as perms when in fact they were combs.

The correct answer to this puzzle is very definitely 715 because the OP said it was a combination.

Or in maths terms

Comb: 13!/4!x(13-4)!
Perm: 13!/(13-4)!

[ollieclarets8]

Gemini literally displays the answer if it's copied and pasted into the Google search

[Bosscat]

I have 13 different things.
I can only choose 4 things.
I must choose 4 things.

How many combinations of things are there?

Screenshot_20250906_123013_Chrome.jpg (211.77 KiB) Viewed 774 times

Screenshot_20250906_123052_Chrome.jpg (241.16 KiB) Viewed 774 times

[ClaretTony]

Screenshot_20250906_123013_Chrome.jpgScreenshot_20250906_123052_Chrome.jpg

Which is exactly what I posted up the thread

[Funkydrummer]

Easy

If it’s a combination, the answer is

13! divided by 4!x9!

Bang on !!!

[maccclaret]

So, if four of the things in a prize draw were Lamborghinis and 9 were bags of penny mix and the tickets were a pound a go, you’d only have to spend £715 to guarantee yourself for Lamborghinis.

You’d struggle to persuade the person on the stall that offering them £750 for the four cars was a good outcome for their charity.

[CnBtruntru]

715

[ollieclarets8]

715

I think we have our winner.

[Foreverly Claret]

This is how the bookies do it
If you had 13 horses and you wanted to know how many four timers there were in multiple bet,the quick way is

13 x 12 x 11 x10 divide by 4 x 3 x 2 x 1 =17160 ÷ 24 = 715

You don't really need the 1 obviously

For doubles the calc 13 x 12 ÷ 2 = 78

For trebles the calc 13 x 12 x11 ÷ 3 x 2 = 286

I think that's right. You take the number of horses in the particular combination eg a fivefold would be 5 x 4 x 3 x 2 x 1 and divide the answer into the product of 13 x 12 x 11 x 10 x 9.
I'm not a bookie !!!!

[Leisure]

This is how the bookies do it
If you had 13 horses and you wanted to know how many four timers there were in multiple bet,the quick way is

13 x 12 x 11 x10 divide by 4 x 3 x 2 x 1 =17160 ÷ 24 = 715

You don't really need the 1 obviously

For doubles the calc 13 x 12 ÷ 2 = 78

For trebles the calc 13 x 12 x11 ÷ 3 x 2 = 286

I think that's right. You take the number of horses in the particular combination eg a fivefold would be 5 x 4 x 3 x 2 x 1 and divide the answer into the product of 13 x 12 x 11 x 10 x 9.
I'm not a bookie !!!!

I can tell!

[Leisure]

This, 715 for combination, 17,160 for permutations

[Malvern claret]

Only just seen this.

CT is spot on, I suspect he had the same outstanding maths teacher as me, a certain Nobby Stokes!

[duncandisorderly]

Well, this caught a bit of traction over the international break, so thank you all!
715. I might tattoo it on a treasured animal by way of remembrance.

Am I to assume that zero got the correct answer within 25 minutes, so wins the ineffable internet points?
I'd like also to assume that No Ney Never (I hope that is misspelt ironically) has learnt a lesson about being a bit nicer on the internet due to all the help I received from other people.
Once again, many thanks. Sometimes things get asked because they're interesting, sometimes because they are important. You don't know why they matter, or to whom they are important but it's important to keep answering.

[GordonvaleClaret]

I’d stick with the 715, the 17,160 is correct if the four selections have to be in the correct order.

So if any order and you select 1-2-3-4 then it is 715 but if you then have 1-2-4-3 etc as extra options then it is 715 x 24 =17,160.

So 715 for combination but 17,160 for permutations.

Mel Saunders would be proud of you!

[ClaretTony]

Mel Saunders would be proud of you!

Mercifully I avoided him when it came to maths - thankful to Jennings & Stokes