Nine pax are to be divided into 4 grps. Find the number of ways this can be done if 1 grp consists of 3 pax and the other 3 grps consists of 2 each. My solution: I will choose 3 out of 9 people first, and then I'll have 6 people left to choose 2 people from and then 4 people left to choose another 2 people from followed by 2 people left to choose 2 people from. 9C3 x 6C2 x 4C2 x 2C2 = 7560. However, the correct answer is 1260 which is 1/6 of the answer I got. Why do we have to divide by 6?
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Hint: Each of the three groups of 2 pax are interchangeable with each other – NickC Feb 15 '22 at 03:52
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1Not pax but packs. Not grp but groups. Please no SMS style. – Jean Marie Feb 15 '22 at 05:27
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1Lucky other responses existed. Saved me from having to google for the mathematical meaning of "pax". – user2661923 Feb 15 '22 at 07:42
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The question/answer has been written with abbreviations, etc in a manner that it is unclear. "pax" presumably means packs, but you have later solved it using people
Reframing it as objects in boxes, it all depends whether the objects and boxes are distinct (labeled) or identical (unlabeled) This always needs to be specified to arrive at the correct answer.
Your answer is correct if packs and groups are both labeled.
The book answer takes the groups to be unlabeled, thus we need to divide by $3!$ as we can't distinguish between the three groups which have identical numbers of packs.
true blue anil
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