Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

**ClassicMan****Member**- Registered: 2014-06-23
- Posts: 4

This time I'm trying to use the 'Combinations and Permutations Calculator' to list permutations of numbers.

This is the calculator I'm using.

Combinations and Permutations Calculator

I want to list the permutations of the following.

9,8,7,6,5,4,3,2,-

(a) The - must appear once or twice in each permutation. For eg. [6,4,-] [-,-,3] [-5,2] and so on.

(b) Pairs of the numbers 9,8,7,6,5,4,3,2, must not be repeated. For eg [7,5,-] is good, but [5,7,-] is not allowed and so on. The - is unaffected by this and can appear repeatedly.

I entered the following into the calciulator.

Permutations without repetition (n=9, r=3)

Is order important: Yes

-,9,8,7,6,5,4,3,2

has 1 of: -,

This gave me almost the list I needed except that pairs of the numbers 9,8,7,6,5,4,3,2 were repeated. For eg, the list gave: [-,9,8] and [-.8,9], the [-,8,9] is not allowed. There were loads of other repeated pairs.

Could any of the rules be used to filter these repeated pairs of numbers and if so how would they be applied?

Many thanks.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,691

Hi;

So you are saying you do not like all of this type,

{-, 9, 4}, {-, 4, 9}, {9,-, 4} etc?

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

Offline