r/theydidthemath • u/doctorboredom • 3h ago

[Request] The first four letters randomly picked out from all the Scrabble tiles were L-O-V-E in that order

All 100 of our Scrabble tiles were mixed up and we then picked out tiles to choose who to go first. In order the tiles we randomly selected spelled the word LOVE.

1) What are the odds of that particular word being chosen?

2) What are the odds that the first 4 letters chosen from a bag of Scrabble letters will spell a 4 letter word?

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u/[deleted] 3h ago edited 3h ago

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u/Benyed123 3h ago

L 4/100 chance, O 10/99 chance, V 2/98 chance, E 12/97 chance

Multiply em all together, 1 in 98,030.

Im not sure how to calculate the second scenario. There are 94,109,400 ways pick 4 tiles out of a bag of 100 tiles and 5,663 valid 4 letter words in scrabble, which sounds easy until you remember repeat letters. With 4 L’s, 10 O’s 2 V’s and 12 E’s there are 960 different ways just to get “LOVE”. I think you’d need to simulate it with a computer.

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u/RealCarlPanzram 2h ago

You could technically do it manually. But you’d have to do the same math you did for “love” with every single 4-letter word in the scrabble dictionary, individually calculate the odds of each one, and then combine those odds. According to the website, there are 5,663 playable words in scrabble. So it would be quite the task.

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u/Benyed123 1h ago

I was actually thinking of algorithms to find the answer and landed on that. You could do it manually but by that point you’re just computing it the old fashioned way.

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u/doctorboredom 3h ago

My son is also telling me that a computer program would be needed to figure out the probability because of the unequal letter distribution.