# Math Help - Inclusion and exclusion question

1. ## Inclusion and exclusion question

Hi
I have the following question and struggling:
let A be the 10-digit decimal integer, that is
A:={0000000000,0000000001,...,9999999999}
How many elements of A have exactly three o's and two 1's?

So i need to use p(a and b)= p(a) + p(b) - p(a or b)
Just struggling to find how many elements there are with exactly what is needed so i can apply it to the equation

2. How many elements of A have exactly three o's and two 1's?
Three 0's and two 1's make 5, not 10, digits. Also, |A union B| = |A| + |B| - |A intersection B|. I think you have "and" and "or" switched.

3. Originally Posted by emakarov
Three 0's and two 1's make 5, not 10, digits. Also, |A union B| = |A| + |B| - |A intersection B|. I think you have "and" and "or" switched.
I think its asking how many combinations are there of exactly 3 o's for example 9999999000 is possible etc and then them same for exactly two 1's, something to do with combinations just can't put my finger on it.

4. Originally Posted by breitling
let A be the 10-digit decimal integer, that is
A:={0000000000,0000000001,...,9999999999}
How many elements of A have exactly three o's and two 1's?
There will be five places for digits other than a 0 or a 1.
Select those places $\binom{10}{5}$. Those can be filled in 8^5 different ways.
From the remaining five places choose two, $\binom{5}{2}$, into which the 1’s go. The zeros go into the remaining places.
Now just multiply.

Edit: Note the and.