Functions are formed from the set A = {a_1, a | vedclass

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(D) The total number of functions from set $A$ to set $B$ is given by $|B|^{|A|}$.Here, $|A| = 3$ and $|B| = 5$.Total number of functions = $5^3 = 125

Vedclass · Accepted Answer

$\frac{12}{25}$

Vedclass · Answer

(D) The total number of functions from set $A$ to set $B$ is given by $|B|^{|A|}$.Here, $|A| = 3$ and $|B| = 5$.Total number of functions = $5^3 = 125$.$A$ function is one-one if each element in $A$ is mapped to a distinct element in $B$.The number of one-one functions is given by the number of permutations of $5$ elements taken $3$ at a time, which is $P(5, 3) = 5 	imes 4 	imes 3 = 60$.The probability that a randomly selected function is one-one is the ratio of the number of one-one functions to the total number of functions.Probability = $\frac{60}{125} = \frac{12}{25}$.

Functions are formed from the set $A = \{a_1, a_2, a_3\}$ to another set $B = \{b_1, b_2, b_3, b_4, b_5\}$. If a function is selected at random, the probability that it is a one-one function is

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