Write total number of one-one functions from set `A={1,\ 2,\ 3,\ 4}` to set `B={a ,\ b ,\ c}` .

Explanation

To find the total number of one-one functions from set \( A = \{1, 2, 3, 4\} \) to set \( B = \{a, b, c\} \), we can follow these steps:

### Step 1: Determine the cardinalities of the sets
- Set \( A \) has 4 elements: \( |A| = 4 \)
- Set \( B \) has 3 elements: \( |B| = 3 \)

### Step 2: Check the condition for one-one functions
A function is one-one (injective) if different elements in the domain map to different elements in the codomain. For a one-one function to exist from set \( A \) to set \( B \), the number of elements in \( B \) must be greater than or equal to the number of elements in \( A \).
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