# Math Help - Question about Probability - Arrange set of Numbers

1. ## Question about Probability - Arrange set of Numbers

Dear all, I was given a set of number "0000011" and asked how many different arrangement I can make with only this set of number.

I tried to list all possible arrangements (0100001, 0001001.......) But it takes way too long. I am think of using the formula of Permutation, am i on the right track?

Thanks!

2. Hello, mak15!

I was given a set of number "0000011"
and asked how many different arrangements I can make with this set of number.
Due to the simplicity of the given number, it is a Combination problem.

We will have a 7-digit number: ._ _ _ _ _ _ _

Select 2 of the position in which to place the 1's.
(The 0's will go in the remaining positions.)

The answer is: . $_7C_2 \:=\:{7\choose2} \:=\:\frac{7!}{2!\,5!} \:=\:21$ arrangements.

3. Thank you so much! But still confused.

If I change "0000011" to "abcdeff", will I use the same formula?

4. Originally Posted by mak15
If I change "0000011" to "abcdeff", will I use the same formula?
No you do not.
In that case you have seven with two repeats. So $\frac{7!}{2!}$.

If you had "10aabbbccccddddd" $\frac{16!}{(2!)(3!)(4!)(5!)}$