Pascals triangle

[Cobra]

I have a question about how to use the numbers in the pascal triangle to determine certain probabilities. Lets assume I have used inclusion-exclusion principle to solve a certain question and have come up with exactly five terms. Do I have the right multiplyers for the following questions.

1. One or more

term one - term two + term three - term four + term five

2. Exactly one

term one-2*term two+3*term three-4*term four+5*term five

3. Two or more

term two - 2*term three + 3*term four - 4*term five

4. Exactly two

term two - 3*term three + 6* term four - 10*term five

5. Three or more

term three - 3*term four + 6*term five

6. Exactly three

term three - 4*term four + 10*term five

Am I doing this correctly.

Thank you,

Cobra

[BruceZ]

[ QUOTE ]
I have a question about how to use the numbers in the pascal triangle to determine certain probabilities. Lets assume I have used inclusion-exclusion principle to solve a certain question and have come up with exactly five terms. Do I have the right multiplyers for the following questions.

1. One or more

term one - term two + term three - term four + term five

2. Exactly one

term one-2*term two+3*term three-4*term four+5*term five

3. Two or more

term two - 2*term three + 3*term four - 4*term five

4. Exactly two

term two - 3*term three + 6* term four - 10*term five

5. Three or more

term three - 3*term four + 6*term five

6. Exactly three

term three - 4*term four + 10*term five

Am I doing this correctly.

Thank you,

Cobra

[/ QUOTE ]

That's correct. You use the same coefficients for "exactly n" as for "n + 1 or more", and the coefficients come from Pascal's triangle with every other term negated as you have shown. This post explains the generalized inclusion-exclusion method, and here is another example.

Did you get this from me? I haven't seen this anywhere else, though I'm sure it must appear somewhere.

[Cobra]

Yes BruceZ I did get this from you. It was about two years ago and when I searched for it I was unable to find it. You were answering some questions on inclusion-exlusion. I thought I remembered it but I just wanted to confirm it. I thought that there was a catch on the last term. Something like if you determine all terms of the probability question that the last term had a different multiplyer. Thanks for your response.

Cobra