1. ## How many combinations?

Suppose I have $\displaystyle a_1,a_1,a_2,a_3,a_4,a_5,a_5$. How many ways can I arrange them?

If I have $\displaystyle a_1,a_1,a_2,a_3,a_4,a_5,a_6$, then I would have $\displaystyle ^7C_2$ combinations. What do I do if I have another group of two?

Would it be $\displaystyle ^7C_3.^4C_2$ (ie. the number of ways of picking $\displaystyle a_2,a_3,a_4$ multiplied by the number of ways of rearranging $\displaystyle a_1,a_1,a_5,a_5$?

2. Originally Posted by Showcase_22
Suppose I have $\displaystyle a_1,a_1,a_2,a_3,a_4,a_5,a_5$. How many ways can I arrange them?
I do not understand this question fully.
But the answer to the quoted part is $\displaystyle \frac{7!}{(2!)^2}$