Each letter in the word $"BRILLIANT"$ were written in $1$ inch by $1$ inch tiles. These tiles were put in a box. If two tiles are drawn at random without replacement, what is the probability that the two letters are the same letters? The answer is in the form $\dfrac{x}{y}$ , where $x$ and $y$ are positive co-prime integers.

Find $3x^{321}+3y^3$ .

The answer is 17499.

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There are $9$ letters in the word

"BRILLIANT".Two letters,

"I"and"L"can be picked twice. So, the number of favorable outcomes is $2$ .The total number of ways of picking two letters from the word

"BRILLIANT"are$\Large{9 \choose 2}$ $=$ $\dfrac{9\cdot8}{2}$ $=36$

So the probability that the two letters are the same letters is Number of favorable outcomes $\div$ Total number of Outcomes

$=$ $\dfrac{2}{36}$

$=\dfrac{1}{18}$ .

Since $1$ and $18$ are co-prime,

$\dfrac{x}{y}=\dfrac{1}{18}$ .

$\implies x=1, y=18$ .

$3x^{321} +3y^3$

$=3\cdot1^{321}+3\cdot18^3$

$=3\cdot1 +3\cdot5832$

$=3 + 17496$

$=\boxed{17499}$