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jaus tail

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## Homework Statement

All permutations made with letters (a, a, b, c) taken two at a time are:

## Homework Equations

Permutation is

^{n}P

_{r}where n is total number of things, r is number of things taken at a time.

If P

_{1}objects are identical, P

_{2}objects are identical such that P

_{1}+ P

_{2}= n

then permutation is

n!/(P

_{1}!P

_{2}!)

## The Attempt at a Solution

Here letters are (a, a, b, c)

Four letters. n = 4.

Taking 2 at a time. means r = 2

But two letters repeat so P

_{1}= 2.

letter b comes once. so P

_{2}= 1

Letter c comes once so P

_{3}= 1

*Permutation is: 4!/(2!)(1!)(1!) = 4 * 3*2/(2) = 12*

But if i arrange the letters I get:

(a, a, b, c) taking 2 letters at a time:

- aa
- ab
- ba
- ac
- ca
- bc
- cb

Whereas by formula I get answer as 12. (above in italics)

PS ( I know I'm posting a lot. But i have a big exam of math and electronics on 11th feb and thus am revising all topics together. )

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