GATE 2015 question on Function (NAT)

Let X and Y denote the sets containing 2 and 20 distinct objects respectively and F denote the set of all possible functions
defined from X to Y . Let f be randomly chosen from  F. The probability of being one-to-one is ______.

Answer

Total functions from set X to Y = 202. (viz. the number of elements in F)

Total one-to-one functions from X to Y = 20*19 

∴ The probability that a chosen function from set F is one-to-one = \( = {20*19 \over 20*20}\) = 0.95

 

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