Seven different coins are to be divided amongst 3 person if no 2 of person recieve same no of coins but each receive atleast one coin n none is left over then nos of ways in which the division can be done is
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We will be using The multinomial expansion to solve this which will be
3 to the power 7 - 3C1 (3-1)to the power 7 - 3C2 (3-2)to the power 7 - 3C3 (3-3)to the power 7
3 to the power 7 - 3C1 (3-1)to the power 7 - 3C2 (3-2)to the power 7 - 3C3 (3-3)to the power 7
rohitdivekar46:
Can u elabrote it plz
its a little difficult to elaborate. I Suggests you to rad and understand the Multinomial expansion which is A part of Binomial expansion. Hope this will help...
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Answered by
20
Well with three people and no two people getting the same number (and everyone gets at least 1)- the only way is to divide it is 1-2-4,,,
Assume person one gets one coin... there are 7 possibilities
Person two gets 2 coins from the remaining 6 = 6!/(6-2)!2!=15 (because the order of the coins doesn't matter)
Person 3 gets what's left - 4 coins (1 possibility again order does not matter)
but there are also 6 ways to arrange the people...
7*15*6=630
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