1Pleaaaaase help out Gotham City Police Dept.....
The no. of ways in which 9 identical balls can be placed in 3 identical boxes is __________________ .
Ans : 12
Neways i'm posting a method which if you can understand .... explain to the Dark Knight so that I can confuse the Joker !!!!! :-)
(3C1 x 2C1 x 1C1) x 2 = 12
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UP 0 DOWN 0 0 4
4 Answers
62I have no idea of what is the logic of the given answer...
May be I am sleeping...
What I can think of is this..
if a=b then a can take values 0, 1, 2, 3, 4 so 5 ways
if none is equal, then
a=0, b,c = (1, 8),(2,7), (3,6), (4,5)
a=1, b,c = (2, 6),(3,5)
if a=2, b,c = (3, 4)
so in all you have 7+5 =12 ways..
62a slightly better method would have been to assume that
a≥b≥c
a=b+t
b=c+m
we have to find the no of solns of a+b+c=9
whihc is same as b+t+b+c=9
which is same as 3c+2m+t=9
now c can take values 0,1, 2, 3
c=0, them m can take 5 values
if c=1, m can take 4 values
if c=2, m can take 2 values
if c=3, m can take 1 value
Hence 12 solns in all..