An easy one (again from AITS)

Let f : A-->B be an onto function where A={1,2,3,4} B = {x,y,z} also f(!) = x

Let M be total such functions then find value of M/2

2 Answers

if f(1) = x

then f(2) can either be x or y or z

same with 3, 4

thus, there are 3³ = 27 such functions....

Out of these, we want only onto functions..
No of functions which dont have z in their range =2³
No of functions which dont have y in their range =2³

No fo functions which dont have both y and z in their range = 1

Thus, M= 27-8-8+1 = 12

M/2 = 6

Thanks Nishant Sir

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