11sorry again
55x12!
In how many ways 12 different fruits can be distributed among 3 boys so each receives atleast one?
just for confirmation....
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9 Answers
13subash...can this 12! be done??
virang din get u :(...explain a bit...
i got 3^12...don know if it is rite
13but the fruits are different...
watz the ans if they are identical??
1luk each apple has got 3 choices so 312...but it doesnt end there as he wants each boy to recieve atleast one apple...so we'l have to discard all cases in which the boys donot get atleast one apple each...for that we concider 2 different cases,
1) in which 1 boy doesnot any apple
2)2 boys donot get any apples..
for the 1st one we have
3C2*(212-2) ways
for the second we have
3C2 ways
so the final answer shud be the initial one -(cases where u donot have justice done to every one)
=312-(3(212-2)+3)
cheers!!
1without any restrictions, each fruit has three choices so number of ways = 3^{12}
Now if one boy does not get any fruit then the number
of ways = ^{3}C_{2}.2^{12}
now if two do not get any fruits then the number of ways =
^{3}C_{1}.1^{12}
Now if none of them get no fruits then number of ways = 1
So, by principle of inclusion and exclusion the answer
is = 3^{12} - ^{3}C_{2}.2^{12} + ^{3}C_{1}.1^{12}-1