Find the number of functions f : A → B where n(a) = m , n(b) = t , which are non decreasing
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ways
Sol. Let A = {a 1 , a 2 , ..... a m } , B = {b 1 , b 2 , ..... b t } with a 1 > a 2 > ....> a m and b 1 > b 2 > ....... > b t
Now for non decreasing function
f(a 1 ) > f(a 2 ) > ..... > f(a m )
where {f(a 1 ) , f(a 2 ) ...... f(a m )} 
{b 1 , b 2 , ..... b t }
Let us introduce (m – 1) dummy numbers C 1 , C 2 , .... C m – 1 and add into the set B, and then take m numbers from the new B in 
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it is the required no. of non decreasing function from A → B.
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