# How many combinations?

• April 5th 2010, 08:07 AM
Showcase_22
How many combinations?
Suppose I have $a_1,a_1,a_2,a_3,a_4,a_5,a_5$. How many ways can I arrange them?

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

Would it be $^7C_3.^4C_2$ (ie. the number of ways of picking $a_2,a_3,a_4$ multiplied by the number of ways of rearranging $a_1,a_1,a_5,a_5$?
• April 5th 2010, 08:26 AM
Plato
Quote:

Originally Posted by Showcase_22
Suppose I have $a_1,a_1,a_2,a_3,a_4,a_5,a_5$. How many ways can I arrange them?

I do not understand this question fully.
But the answer to the quoted part is $\frac{7!}{(2!)^2}$