Question

The number of one-one functions \( f: \{1, 2, 3\} \to \{a, b, c, d, e\} \) is:

• A. 125
• B. 60
• C. 243
• D. None of the above

Hint:

For a one-one function, the number of ways to assign values is the product of the available choices at each step.

Answer 1

The Correct Option is B

To find the number of one-one (injective) functions from a set of 3 elements to a set of 5 elements, we need to assign distinct elements from the range set to the elements in the domain.

Step 1: Total Elements in Domain and Codomain
The domain has 3 elements 1, 2, 3 and the codomain has 5 elements a, b, c, d, e.

Step 2: Assign Values to Each Element
Since we need a one-one function, each element in the domain must map to a distinct element in the codomain.
For the first element in the domain (1), we have 5 choices from the codomain (a, b, c, d, e).
For the second element in the domain (2), since the function is one-one, we have 4 remaining choices.
For the third element in the domain (3), we have 3 remaining choices.

Step 3: Total Number of Functions
To calculate the total number of one-one functions, multiply the number of choices for each element:
\[ \text{Total number of one-one functions} = 5 \times 4 \times 3 = 60 \]
Thus, the correct answer is:
\[ \boxed{60} \]