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There are 9 seats in a row, 3 Chinese people.. 3 Russians and 3 Poles. How many ways are there for those people to be seated, so that they don't sit next to a person of the same nationality.

Would anyone be so kind, so as to tell me if this is the answer?

6*4*2=48

user211302
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1 Answers1

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48 is not the answer.

First let's figure out how many options you have for each selection.

The first seat is available for anyone to sit in, so there are 9 possible selections. The second seat is a little trickier, normally there would be 8 remaining options, but to take into account the 2 remaining people of the same nationality of the previous seat, we must subtract them from the possible selections for seat number 2....this gives us 6 possibilities. Continue this pattern down to the last seat, and multiply all the options for each seat together to find the answer. The number will be a lot larger than your original answer.

Mike
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  • Appreciated Mike.. would you mind telling me if this is it? 965443221? – user211302 Jan 28 '15 at 19:36
  • That looks right, so 51840 possible permutations....and we aren't dividing by anything since all of the people are being picked. kind of like a "pick 9 out of 9" which would be 9!/0!. Modified to fit the stipulations of this particular question. – Mike Jan 28 '15 at 20:14
  • well technically we are dividing by 0!, which is 1 so the answer is 51840/1 = 51840. – Mike Jan 28 '15 at 20:20
  • Be careful at the fourth step. Suppose you have selected a Russian for the first seat and a Chinese for the second seat. There are five choices for the third seat since there are three Poles and two Russians available. If you have selected a Pole for the third seat, there are now four choices for the fourth seat - the two remaining Russians and two remaining Chinese. If you have selected a Russian for the third seat, there are still five choices - the two remaining Chinese and the three Poles. – N. F. Taussig Jan 29 '15 at 15:59
  • Ahh, my answer may be incorrect then. I'm still a novice at this aswell so I'm not quite sure at this point. – Mike Jan 30 '15 at 16:31