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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 nPr where n is total number of things, r is number of things taken at a time.
If P1 objects are identical, P2 objects are identical such that P1 + P2 = n
then permutation is
n!/(P1!P2 !)
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 P1 = 2.
letter b comes once. so P2 = 1
Letter c comes once so P3 = 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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