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In how many different ways can the letters A, A, B

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Re: In how many different ways can the letters A, A, B [#permalink] New post 26 Jun 2013, 14:10
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Possible arrangements:
1) xcxxxxxx ---- 1C1 * 6!/(2!*3!) (D can be placed in 1 position)
2) xxcxxxxx ---- 2C1 * 6!/(2!*3!) (D can be placed in 2 positions)
3) xxxcxxxx ---- 3C1 * 6!/(2!*3!) (D can be placed in 3 positions)
4) xxxxcxxx ---- 4C1 * 6!/(2!*3!) (D can be placed in 4 positions)
5) xxxxxcxx ---- 5C1 * 6!/(2!*3!) (D can be placed in 5 positions)
6) xxxxxxcx ---- 6C1 * 6!/(2!*3!) (D can be placed in 6 positions)
7) xxxxxxxc ----- 7C1 * 6!/(2!*3!) (D can be placed in 7 positions)

Adding them all
= (1+2+3+4+5+6+7) * 6!/(2!*3!)
= 28 * 6!/(2!*3!)
= 1680
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Re: In how many different ways can the letters A, A, B [#permalink] New post 26 Jul 2014, 20:08
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Re: In how many different ways can the letters A, A, B   [#permalink] 26 Jul 2014, 20:08
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