Puzzle 5

You are an assistant game designer working on a word game.
At the start of the game, the player draws some tiles from the bag.
The lead designer asks the lead programmer to add a special feature that
prevents the player from ever getting an opening hand of all vowels
or all consonants.

But the lead programmer is too busy, so the lead designer tells you to
figure out how often the player will get an opening hand of all consonants
or all vowels, assuming a hand size of 6, 40 vowels, and 60 consonants.
Then the lead designer asks you to figure out what you would change to
make that chance less than one game in a million.

Hand Size (tiles)
How many vowel tiles?
How many consonant tiles?

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