Math calculation

Hello, wanted to check the odds of this happening. A friend recently lost his wife. They liked to play scrabble, and the first time playing with his daughter the tiles spelled her unique 1st name VYETTE, the other letter was a U. They are a deeply religious family and I like to believe this is some sort of miracle. There is also a picture of the board.

My friends daughter picked first, the picture shows she had a "L" "A" "W" "blank tile" "E" "R" , not sure of 7th tile.

My friend then picked "U" "V" "Y" "E" "T" "T" "E"

There are 100 tiles in the scrabble game.
12-E's
6- T's
4- U's
2- V's
2- Y's

WHAT IS THE PROBABILITY OF THIS HAPPENING ?

I get 1 in 48314.

This assumes that the 7th letter can be anything. Although unlikely, it is possible without divine intervention.

Thanks, this is what I calculated for all 7 letters, but I don't know how to calculate without knowing exactly what his daughter's 7th letter was, but assumed it was not one my friend picked.

With 7 tiles already picked already, there are 9,473,622,444 possible remaining combinations of tiles.

With a "E" already picked by his daughter. I came up with 13,200 ways to get UYVETTE.

So with "U" included, all 7 tiles picked I came up with 1 in 717,698.

Is this math correct?

Quote: ChiTownJoe

So with "U" included, all 7 tiles picked I came up with 1 in 717,698.

Is this math correct?

Yes.

If, however, the last letter can be anything and you know that the first player has picked an E, the probability is 1 in 37,122.

Thanks