# Counting Permutations

## Homework Statement

How many 3 digit numbers can be constructed from digits 1, 2, 3, 4, 5, 6, and 7 if each digit may be used once only and the number is odd?

2. The attempt at a solution
What number do they speak of? The resulting 3 digit number? How do I approach this equation?

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olgranpappy
Homework Helper

## Homework Statement

How many 3 digit numbers can be constructed from digits 1, 2, 3, 4, 5, 6, and 7 if each digit may be used once only and the number is odd?

2. The attempt at a solution
What number do they speak of? The resulting 3 digit number? How do I approach this equation?
For example, I could pick out the numbers 1,2 and 3 and form the number

123

but also, I could form, 132 ,or 213, or 231, or 312, or 321.

But, that is just one way to pick three numbers (1,2,3). I could have chosen to pick out the numbers 3,5 and 1. And I could then form 6 different numbers (135,153,315,351,513,531) with those.

If I were you I would start off by thinking about how many different ways there are to choose three different things out of an array of 7 different things. "Seven choose three".

Then, you know that for any set of three, you can make 6 numbers, but you have to figure out how many of them are odd. Good luck.

olgranpappy
Homework Helper
What number do they speak of?

Oh. Yeah. They are probably talking about the *resulting* number (the three digit number). That is a very confusing way to word the problem. It is certainly vague.