Basic combinatorics question, can you help me?

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Before I start let me thank anyone that contributes to helping me with an answer for this. Ok - on to the question. Assume you have 10 jelly beans, 5 yellow and 5 red. What is the total amount of ways that they can be arranged in a line assuming there is no difference between the jelly beans within a specific colour? Another way of saying this is 'I have two jelly beans of different colours, they get placed back to be chosen from again after use. How many different combinations can be made?' Thanks everyone.

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You have $10$ placeholders, and you choose the $5$ places where the yellow beans will go: ${10 \choose 5}=252$ possibilities.


Regarding the second statement and your comment:

If, by Catalan word, you actually mean Dyck word, then the answer is easy: for a length $2n$, you have ${2n \choose n}$ possible words with two symbols, out of which $C_n$ are Dyck words, with $C_n$ the Catalan numbers:

$$C_n=\frac1{n+1}{2n \choose n}$$

So your probability would be $\dfrac1{n+1}$.