Re: permutation
[#permalink]
04 Oct 2009, 06:34
Hi appuamar,
Your post was a little hard to read--may I suggest cutting and pasting problems, rather than paraphrasing?--but I think I've got a solution.
The PM, MP, and MLA always speak in that order, though at possibly spread out among the ten positions. the means there are 10C3 ways to place those three speakers (i.e. PM 1st, MP 2nd, MLA 3rd; PM 1st, MP 2nd, MLA 4th...)
10C3 = 10! / 3!(10-3)! = 10*9*8 / 3*2 = 120. There are 120 ways to arrange the PM, MP, and MLA.
Now, I can't tell from your transcription of the problem as to whether this is the answer to the question, or whether it is looking for the ways to arrange all 10 speakers. If we need to arrange all 10, then the remaining 7 speakers can be ordered in 7! = 7*6*5*4*3*2 = 5040 ways. However, as the final result ends up being over 600,000, it doesn't strike me as a very GMAT-like answer.
FInally, on the GMAT, there is a strong possibility that we could eliminate trap answers or use common sense to make this problem much less math-intensive. What were the answer choices?