GATE | GATE-CS-2015 (Set 2) | Question 65

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 and Y. Let f be randomly chosen from F. The probability of f being one-to-one is _________
(A) 0.95
(B) 0.80
(C) 0.75
(D) 0.70


Answer: (A)

Explanation: X has 2 elements
Y has 20 elements

Number of functions from X to Y is 20*20
[Every element can take any of the 20 values]

Number of one to one functions from X to Y is 20*19
[Every element takes a different value]

So probability of a function being one to one
= (20*19) / (20*20)
= 380 / 400
= 0.95

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