The number of one-to-one functions from to is:

Explanation: Let set and set . Number of elements in , Number of elements in , For a function to be one-to-one (injective), each element in the domain must be mapped to a distinct element in the codomain . Number of one-to-one functions is given by: Correct Option: (d)

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NIMCET 2015 — Mathematics PYQ

NIMCET | Mathematics | 2015

The number of one-to-one functions from $\{1, 2, 3\}$ to $\{1, 2, 3, 4, 5\}$ is:

Choose the correct answer:

Explanation

Let set $A = \{1, 2, 3\}$ and set $B = \{1, 2, 3, 4, 5\}$ .

Number of elements in $A$ , $n(A) = 3$

Number of elements in $B$ , $n(B) = 5$

For a function to be one-to-one (injective), each element in the domain $A$ must be mapped to a distinct element in the codomain $B$ .

Number of one-to-one functions is given by:

$P(n(B), n(A)) = \, ^{n(B)}P_{n(A)}$

^{5}P_{3} = \frac{5!}{(5-3)!}

^{5}P_{3} = \frac{5 \times 4 \times 3 \times 2!}{2!}

^{5}P_{3} = 5 \times 4 \times 3

^{5}P_{3} = 60

Correct Option: (d)