Bingo Probability question - no numbers under one letter.

We have a bingo fundraiser going at work and I think there's a problem, but I need someone who understands statistics to help me prove it. We're playing for certain shapes on the card - like 'T', 'H', 'I', 'X' and full card. The last game was for the H, so the numbers under the N were all removed from play as we only needed the free space under N to win. Now we're playing for the I, so we need more numbers under the N than any other letter. So far they've drawn 12 numbers with none under the N. Because of this I believe they forgot to put the numbers under the N back into the hopper to be drawn.

So the question is this: What is the probability that you can draw 12 bingo numbers with none of them falling under one particular letter?

My stats knowledge is weak, so I don't even know where to begin. I can figure out that 12 numbers drawn out of 75 numbers available is 16% of the numbers drawn. That's easy.

• en.wikipedia.org/wiki/Hypergeometric_distribution Assuming there are $15$ balls for each letter, five letters for a total of $5\cdot 15 = 75$ balls, the probability that twelve balls drawn all are not of a specific letter (in this case N) would be $\dfrac{\binom{15}{0}\binom{60}{12}}{\binom{75}{12}}$ Commented Oct 10, 2019 at 14:03
• so if I read your link right and run the numbers through that equates to 0.053566252? That seems to prove my point that some of the balls are not likely in the hopper. Thanks for the help! Commented Oct 10, 2019 at 14:42