Can someone please explain the difference nCr and nPr…i keep making mistakes with these problems. I understand that nPr is used when order is important…but I can’t seem to figure in what problems the order is important…Like picking 6 people to receive 1st, 2nd and 3rd price can be done in 120 ways…why is order important here???
order matters in that case by definition. There can only be ONE 1st place winner, ONE 2nd place winner, etc. You can’t have 3rd, 1st, 2nd - has to be 1st, 2nd, 3rd in that order.
yea it doesnt make sense thant when I use the order doesnt matter function, ncr, it gives less ways than the order does matter function, npr on my HP. What am i doing wrong?
Let’s take an example of a soccer league with 18 teams. If the rules say that every team plays 1 match against all the other teams, 153 matches will be played in total (it does not matter which team plays in its home stadium, Team1:Team2 and Team2:Team1 is the same). - the order does not matter, nCr However teams start complaining that the HOME team has an unfair advantage over the AWAY team. So it does matter if the game is Team1:Team2 or Team2:Team1. This way every team will play 2 matches against all the other teams. - the order does matter, nPr, 306 matches will be played in total Hope this made it a bit more clear and did not confuse you even more.
yeah, agree with Bill, it seems counterintuitive…you’d think when order matters there would be less possibilities, as opposed to any order of possibilites within the group
take an example: 1234, 4 choose 2 - nCr - 6ways: 12 (same as 21) - since order doesn’t matter these two combos count as only 1 34 (same as 43) 13 (same as 31) 24 (etc…) 14 32 nPr - 12 ways: the 6 from above *plus* 21 43 31 42 41 23
that helps, thanks!
I think if you remember the equations it seems more intuitive. nCr = n!/[(x!)(n-x)!] which has the extra (n-x)! term in the denominator, which will obvioulsy decrease the outcome. In nCr, 1-2-3 is the same as 3-2-1, not so with nPr.
just want to correct a little bit here, nCx has extra x! term in the denominator, not the extra (n-x)! term. nCx= n!/x!(n-x)! nPx= n!/(n-x)! BizBanker Wrote: ------------------------------------------------------- > I think if you remember the equations it seems > more intuitive. nCr = n!/[(x!)(n-x)!] which has > the extra (n-x)! term in the denominator, which > will obvioulsy decrease the outcome. In nCr, 1-2-3 > is the same as 3-2-1, not so with nPr.
Yep thats what i get for posting without the book in front of me. Hopefully this will be pounded into my head in the next 10 days.
you don’t even need to know the formula if you can type it into your calculator.
Besides combinations and permutations I’d also look at labeling: 8 stocks in a portfolio, 4 long term holds, 3 short term holds, and 1 sell. 8! ways to be labeled, 4! ways to be labeled as long term, 3! to be labeled as a short term hold, and 1! to be labeled as sell. 8!/(4!*3!*1!) = 280 ways Formula: n!/[(n1!)*(n2!)*(n3!)*…*(nk!)]
Think of it this way. I’ve found this logic to stick when I’m doing those questions. Say there are three friends, Mike, Mark, and Mindy. They are going to have a race. If order doesn’t matter, there is only one combination. One is 1st, one is 2nd, 1 is 3rd. If order DOES matter, there are 6 different permutations of the event. Order matters because they are being ranked relative to the other racers. It should seem intuitive that there will be more permutations than combinations, and not vice versa. If this doesn’t help, just do what the other guy said and smash it into your BAII
viper: I use the following to overcome this confusion: 1st can be picked in 6 ways; 2nd can be picked in 5 ways; 3rd can be picked in 4 ways. total number of ways to pick is 6*5*4.
How can we calculate this on BAII Plus?
use “2nd followed by -”