1sorry but not quite :(
Consider two sets of distinct real numbers A and B
such that
A={A1,A2,...A100)
B={B1,B2,....B50)
Consider all kinds of onto mappings from set A to set B such that
f(A1)≤f(A2)≤....f(A100)
Find the number of such mappings.
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9 Answers
9isnt it
no of positive int sols to
X1 + X2 + .......X50 = 100
1hmmm.... but you see as the function is onto..
X1,X2,X3....X50 all must be at"least" 1
so we have
X1>=1
=> X1-1>=0
so we take x1-1=t1 x2-1=t2 ....
we get
t1+t2+t3+t4+...........t50=50
no. of possible solutions = 50+50-1C50-1=99C49=99C50
9OMG i had interchanged the formulae
2 months leave has made me forget these formulae which i used to rem even when asked in sleep :(
1we know dat for every selection of 100 elements from B, atleast 1 of each kind, we have an ascending ordered arrangement..
so our task is basically, to select 100 objects out of 50 different kinds of objects, with unlimited supply of each kind of object..., where we have to atleast pick up 1 object of each kind..
so
mathematically we need the coefficiant of x100
in the expansion of
(x+x2+x3+x4....)50
ie coeff of x100
in
x50(1-x)-50
ie
coeff of x50in (1-x)-50
=99C50
cheers!!!
