Question

P(N,K)=N(N-1)(N-2)....(N-P+1): WHERE DOES THE 1 IN N-P+1 COME FROM????

Answer 1

Hey Sarah, looks like a weird boo boo in your problem.
That should be N-K+1, right?

Answer 2

\[\large\rm P(N,K)=\frac{N!}{(N-K)!}\]

Answer 3

We can rewrite the numerator, expanding it out,\[\large\rm P(N,K)=\frac{N(N-1)(N-2)\cdot\cdot\cdot(N-K+1)(N-K)!}{(N-K)!}\]N-K+1 is the value one larger than N-K.
So in our expansion of factorial, that's what shows up next to the N-K.

Answer 4

And then of course you have a nice cancellation,\[\large\rm P(N,K)=\frac{N(N-1)(N-2)\cdot\cdot\cdot(N-K+1)\cancel{(N-K)!}}{\cancel{(N-K)!}}\]

Answer 5

What do you think? Confusing?
@EtherealSarah

Answer 6

THANK YOUU! I've been trying to figure this out for days! And yes, I typed P instead of K by mistake! :3

Answer 7

zepdrix another question: nCr=n!/(n-r)!*r! I don't understand why we add the r! in the denominator , I mean for example if we have 53 cars racing, and we want to know the possible combinations of the three racers that arrive first, we'd do : 53!/(53-3)! , we divide by 50! cuz we only need 3 places right, so all we'll be getting in the end is : 53*52*51 , so why the 3! ?

Answer 8

There are k! ways to arrange things in different order. Since we are not concerned about ordering of things when using nCr, we must divide k! to "collapse" the combinations with the same element but in different order.