Sorry your browser is not supported!

You are using an outdated browser that does not support modern web technologies, in order to use this site please update to a new browser.

Browsers supported include Chrome, FireFox, Safari, Opera, Internet Explorer 10+ or Microsoft Edge.

Geek Culture / Maths help - Permutations and Combinations

Author
Message
Hodgey
15
Years of Service
User Offline
Joined: 10th Oct 2009
Location: Australia
Posted: 13th Nov 2012 08:24
Link
I've come across two unusual questions. I know the answers but I can't work out how to arrive at them (I have spent some time trying to work it out). Since you guys are excellent when it comes to maths, I thought I'd ask.

Q1: The number of sequences of the digits a b c d e f such that:
1 <= a < b < c < d < e < f <= 8

Answer


Q2: The number of sequences of the digits a b c d e f such that:
1 <= a <= b <= c <= d <= e <= f <= 5

Answer


Cheers

Back to top
Profile PM Email
BatVink
Moderator
22
Years of Service
User Offline
Joined: 4th Apr 2003
Location: Gods own County, UK
Posted: 13th Nov 2012 09:02
Link
I have the answer in a book called innumeracy (brilliant read), but by the time I find it, somebody who actually knows the answer will have replied.

Back to top
Profile PM Email
Hodgey
15
Years of Service
User Offline
Joined: 10th Oct 2009
Location: Australia
Posted: 13th Nov 2012 11:07
Link
Quote: "I have the answer in a book called innumeracy (brilliant read), but by the time I find it, somebody who actually knows the answer will have replied."

I appreciate the effort BatVink. If I ever come across that book in the shops I just might get it. My current maths text book for this subject is a little on the thin side.

Back to top
Profile PM Email
Hodgey
15
Years of Service
User Offline
Joined: 10th Oct 2009
Location: Australia
Posted: 13th Nov 2012 23:55 Edited at: 13th Nov 2012 23:56
Link
I worked it out! The answer was right infront of me.

For Q1 you have 8 possible choices (1, 2, 3,...,8) and you need 6 of them (each different so no repetitions) hence 8 "choose" 6 works.

For Q2, similar as above (5 options, 6 choices) except repetitions are allowed which makes it (6+5-1) "choose" 6
= 10! / ((10-6)!*6!)
= 210

I guess the questions were in a form that was foreign to me.

Back to top
Profile PM Email
Libervurto
18
Years of Service
User Offline
Joined: 30th Jun 2006
Location: On Toast
Posted: 15th Nov 2012 22:25 Edited at: 15th Nov 2012 22:25
Link
I couldn't work it out so I wrote them out and it is indeed 28 for Q1. What does 8 "choose" 6 mean?



Shh... you're pretty.
Back to top
Profile PM Email
Hodgey
15
Years of Service
User Offline
Joined: 10th Oct 2009
Location: Australia
Posted: 16th Nov 2012 00:00
Link
Quote: "What does 8 "choose" 6 mean?"

Sorry, I should have explained that more. I couldn't write the short hand notation on the forums. It's a binomial coefficient and is equal to:

8! / ((8-6)!*6!)

The general formula is
n! / ((n-k)!*k!)

which is the number of ways to choose k things from n things.

When I'm talking out loud I just refer to this as "n choose k". It helps conceptually as well.

Back to top
Profile PM Email
Neuro Fuzzy
17
Years of Service
User Offline
Joined: 11th Jun 2007
Location:
Posted: 16th Nov 2012 00:40
Link
Probably good to note that you're talking about combinations, whereas "sequences" usually refers to "permutations".

Back to top
Profile PM Email
Hodgey
15
Years of Service
User Offline
Joined: 10th Oct 2009
Location: Australia
Posted: 16th Nov 2012 01:00
Link
Quote: "Probably good to note that you're talking about combinations, whereas "sequences" usually refers to "permutations"."

Good point. Interestingly when I first saw this question in a quiz, it was multiple choice (the options were of both perms and combs), I assumed permutations and so chose the answer according to that. You can probably tell I got it wrong. Note that the questions aren't my wording.

Cheers

Back to top
Profile PM Email
Neuro Fuzzy
17
Years of Service
User Offline
Joined: 11th Jun 2007
Location:
Posted: 16th Nov 2012 08:27
Link
Huh, that's a pain!

Back to top
Profile PM Email
Back to top

Login to post a reply

Server time is: 2025-05-20 17:04:23
Your offset time is: 2025-05-20 17:04:23