Let

#elements in co-domain = m

#elements in domain = n

#one-to-one functions = P( m, n )

#total functions = m^{n}

probability = P(m,n ) / m^{n}

29 votes

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 $f$ being one-to-one is ______.

42 votes

Best answer

5 votes

Total functions from X to Y = [Order(Y) ]^{order(x)}

and number of one-one functions = ^{20} P _{2}

so probability = number of one one functions / total number of functions = 20*19/20*20 = 0.95