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Posted on 2011-10-28

How many different strings can be formed by rearranging the letters in the word ABABA ? Thanks.

I guess its a combination not permutation because it dont say anything about order

5!

but how to i put into the formula as i need 2 numbers

C(n,r)=n!/r!(n-r)!

I guess its a combination not permutation because it dont say anything about order

5!

but how to i put into the formula as i need 2 numbers

C(n,r)=n!/r!(n-r)!

8 Comments

For more than two different symbols, divide n! by the product of the factorials of the occurrences of the different symbols.

There are 3! options to arrange the 3 As, and 2! to arrange the 2 Bs.

So theres 5!/(3!*2!) options for ABABA.

so: n=5, r=3 or 2 as 5-3=2 and 5-2=3

The result is 10.

ABABA

BAABA

BAAAB

ABAAB

AABAB

AAABB

BBAAA

BABAA

this one is tricky because you have repeated characters. the answer is different than if it were ABCDEF, because as you rearrange them two A's or two B's are indistinguisable.

So it's not just a combination or permutation.

In this case it's probably easiest to just list them all

AAABB

AABAB

AABBA

ABAAB

ABABA

ABBAA

BAAAB

BAABA

BABAA

BBAAA

And note that it doesn't say anything about length: A AA AAA are all possible strings.

This is a different sort of problem.

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