(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let A = {1,2,3} and B = {1,2,3,4,5}

Find the number of functions f: A -> B so that f(1) = f(2)

2. Relevant equations

3. The attempt at a solution

I'm just reviewing random questions for my final on Tuesday and I came upon this question. Seems to be a counting question, and I'm not that sure how to do this since counting questions are more intuition than method (at least that's what I think). Here's what I got:

So a function sends an element from 1 set to another.

There are 3 possible values for the f function, namely f(1), f(2), and f(3).

There are 75 possibilities (5*5*5). So I guess you have to pick the possible values of f(1), f(2) and f(3). So f(1) has 5 choices, f(2) has 1 choice because it must match what f(1) was mapped to, f(3) can be whatever, so it's 5 again.

5 * 1 * 5 = 25

So there are 25 possible functions.

Is this correct? I always hated counting problems ><

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Function counting question

**Physics Forums | Science Articles, Homework Help, Discussion**