Easy Permutations and Combinations

I’ve always confused “permutation” and “combination” — which one’s which?

Here’s an easy way to remember: permutation sounds complicated, doesn’t it? And it is. With permutations, every little detail matters. Alice, Bob and Charlie is different from Charlie, Bob and Alice (insert your friends’ names here).

This is a companion discussion topic for the original entry at http://betterexplained.com/articles/easy-permutations-and-combinations/

[…] (Brush up on combinations and permuations if you like). […]

Thanks alot! This was actally a better explanation then my teacher could give us =]

Awesome! Glad you found it useful :slight_smile:

finally this makes sense

this is an awesome site!

Thanks a million! It makes sense now!

Thanks for the comments, glad you found it useful.

If my chances are 1 in 13 million of winning the lottery and I buy 10 tickets, do my chances increase?

Hi D, when you buy multiple tickets you would add up the chances. So 10 tickets would be 1/13,000,000 + 1/13,000,000 + 1/13,000,000 … = 10 / 13,000,000

So buying multiple tickets would increase your chances for that particular lottery. If you somehow bought half of the available tickets, you’d have a 50-50 chance. And if you bought all of the tickets you’d win :).

I’m having a stupid moment. I have a problem: how many combinations exist when one needs to select a team of 22 players from a squad of 40 players?

IS this 40!/22!(18!) = 113,380,261,800?

It seems a rediculaously large number! Please help me!

Hi David, yep, you got the formula right. The number of permutations (ways to order 22 people of 40) is:

40 * 39 * 38 … * 24 * 23 * 22 * 21 * 20 * 19 = 40! / 18!

[Be careful of off-by-one errors, I had a mistake at first. 40 to 19 is 22 people (just like 40 to 39 is 2 people, even though 40-39 is 1)]

And the number of ways to re-arrange 22 people = 22!

So we divide the first by the second and get

40!/18!(22!) = 113,380,261,800

113 billion does seem huge, but there’s a lot of multiplications happening. There’s 56 ways to pick 3 people from 8, which seems pretty large as well.

It’s one of those things where human beings (all of us!) aren’t great at intuitively estimating the impact of exponential growth. The birthday paradox and the effect of compound interest are other examples of this. I think it’s because we don’t encounter such mind-boggling growth or large numbers in a way we can really experience (at a certain point, millions, billions, and trillions become “a lot”, even though a trillion is a million times bigger than a million).

Great Stuff! You should write a book!

Thanks for the encouragement Aaron! Once I have enough posts I would love to turn it into a book :slight_smile:

it was really useful dude!!!
thnx a lot!!!

No problem, glad it helped!

I play in a fantasy footfall league. I can select players for my team and they each earn points based on their performance in each weeks actual football game. I compete against other teams owners in my league and the owner with the most points each week wins. Also the points earned each week are totaled at the end of the year and the owner with the most points wins the annual point competition.
Of course there are limitations and rules to the game. Of all the players listed I may select only 22 players. Of the 22 players the team must be composed of:

3 quarterbacks (QB)(58 QBs)
6 running backs (RB)(81 RBs)
6wide receivers (WR)(125WRs)
2 tight ends (TE)(56 TEs)
3 kickers (K)(37Ks)
2 defenses (D)(32Ds)

Also each player is assigned a salary and my salary limit for the team is $60,000,000.00 for all 22 players.
I can trade for additional players each week but I’m limited to 120 trades for the year.

Here is the question?:

??? Of all the players available which ;
2QB+6RB+6WR+2TE+3K+2D whose total salary does not exceed $60,000,000 will generate the most projected points???

The program should list the top 20 combinations in descendinding order of points.

Attached is a file that lists all players available. Of all the columns available the only ones used will be Name (player), Salary (in thousands) and PNTS ( projected points for the in todays game).

I think your program PermutCombine will do some of the work but I’

Thanks again for your interest. Sam Eismont

if a train has 18 cars , and 3types of cargo must be transported, how many ways can the 3 types be transported if one type of cargo can at most occupy only ten cars per train?

Thanks alot!!!
am studying n i have an exam 2mmorow !!
thnx 4 helpn me

Hi Besho, I’m glad I was abble to help!