Question

Can you explain how to get to the formula for number of permutations when

1)1 item is always excluded.
2)one item is always is included.

Answer 1

@Miracrown

Answer 2

1 item exclude :
\[^{(n-1)}p_{r}\]

1 item include :
\[^{(n-1)}p_{r-1}\]

Answer 3

you're talking about them ?

Answer 4

Yes I know that

Answer 5

I mean how to understand it logically.

Answer 6

Let me see if I understand the question completely .
Suppose we want to know how many permutations there are using the numbers 1,2,3,4,5,6 where we choose 3 of those numbers and one of the numbers must be a 6 .
Is that like questions #1 ?

Answer 7

whoops , that is like #2 . Is that correct ?

Answer 8

Is the example that I wrote similar to what you are asking about in #2 ? @OptimusPrime_

Answer 9

excluding 1 item means, forget about that item. assume that there are only \(n-1\) items

Answer 10

Yes

Answer 11

okay @rational

Answer 12

Are we done with excluding part ?

Answer 13

alrighty, Do you know the formula for permutations ( n P r ) ?

Answer 14

I think so @rational
@Miracrown yes.

Answer 15

analyze the inclusion same way

Answer 16

ok let's do the specific numerical example I wrote first, then we will move into the more general case

Answer 17

actually, inclusion is bit trickier than that

Answer 18

Suppose we want to know how many permutations there are using the numbers 1,2,3,4,5,6 where we choose 3 of those numbers and one of the numbers must be a 6 .

Answer 19

Yeah I actually knew the exclusion part.

The formula for inclusion given in my text is:

r times (n-1)P(r-1)

Answer 20

we know one of the 3 numbers chosen must be 6 so, really, the only numbers left to choose from would be 1,2,3,4,5 and of those 5 remaining, how many left are there to choose , knowing 6 is already one of the 3 chosen ?

Answer 21

okay @Miracrown

Answer 22

n-1 pr-1 ?

Answer 23

well the perfect way to understand is sketch