Let A be a set containing 10 distinct elements then the total number of distinct functions from A to...........

Let A be a set containing 10 distinct elements, then the total number of distinct functions from A to A is

101

10¹⁰

2¹⁰

2¹⁰-1

Alright, let's break this down:

- We have a set A with 10 distinct elements.

- We're asked: How many distinct functions can we make from A to A?

- For each element in A (that's 10), you can choose any of the 10 elements in A as its image under the function.

- That means 10 choices for the first element, 10 for the second, ..., 10 for the tenth.

- So you multiply: 10 × 10 × ... (10 times) = 10^10 options.

- So, Option 2: 10¹⁰ is the number we want.

Now, the other options:

- Option 1: 101 — That's just a number, no math behind it in this context.

- Option 3: 2¹⁰ — This would be right if we were counting subsets, not functions.

- Option 4: 2¹⁰-1 — That's the count of non-empty subsets of a 10-element set. Again, not functions.

What this really means is: every input has 10 possible outputs, so you get 10^10 total functions.

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