Show me a random blog post


draughts golden ratio trigonometry pac-man statistics video games latex captain scarlet plastic ratio braiding coins sport dates martin gardner map projections craft asteroids christmas puzzles folding tube maps games menace national lottery noughts and crosses reuleaux polygons logic error bars countdown javascript fractals propositional calculus rugby folding paper chebyshev arithmetic realhats estimation polynomials curvature christmas card european cup matt parker game of life golden spiral rhombicuboctahedron machine learning graph theory sorting dragon curves pythagoras binary php football probability inline code interpolation game show probability weather station frobel go chess mathslogicbot triangles news aperiodical big internet math-off london underground world cup flexagons people maths oeis a gamut of games reddit approximation tennis stickers london nine men's morris data books platonic solids bodmas wool speed electromagnetic field dataset programming hats mathsteroids radio 4 bubble bobble palindromes hexapawn chalkdust magazine the aperiodical sound manchester geometry light royal baby harriss spiral cross stitch gerry anderson twitter misleading statistics ternary manchester science festival final fantasy pizza cutting accuracy python raspberry pi


Show me a random blog post
▼ show ▼

Countdown probability

On Countdown, contestants have to make words from nine letters. The contestants take turns to choose how many vowels and consonants they would like. This got me wondering which was the best combination to pick in order to get a nine letter word.
Assuming the letters in countdown are still distributed like this, the probability of getting combinations of letters can be calculated. As the probability throughout the game is dependent on which letters have been picked, I have worked out the probability of getting a nine letter word on the first letters game.

The probability of YODELLING

YODELLING has three vowels and six consonants. There are 6 (3!) ways in which the vowels could be ordered and 720 (6!) ways in which the consonants can be ordered, although each is repeated at there are two Ls, so there are 360 distinct ways to order the consonants. The probability of each of these is:
$$\frac{21\times 13\times 13\times 6\times 3\times 5\times 4\times 8\times 1}{67\times 66\times 65\times 74\times 73\times 72\times 71\times 70\times 69}$$
So the probability of getting YODELLING is:
$$\frac{6\times 360\times 21\times 13\times 13\times 6\times 3\times 5\times 4\times 8\times 1}{67\times 66\times 65\times 74\times 73\times 72\times 71\times 70\times 69} = 0.000000575874154$$

The probability of any nine letter word

I got my computer to find the probability of every nine letter word and found the following probabilities:
ConsonantsVowelsProbability of nine letter word
So the best way to get a nine letter word in the first letters game is to pick five consonants and four vowels.

Similar posts

Countdown probability, pt. 2
Pointless probability
World Cup stickers 2018, pt. 3
World Cup stickers 2018, pt. 2


Comments in green were written by me. Comments in blue were not written by me.
 Add a Comment 

I will only use your email address to reply to your comment (if a reply is needed).

Allowed HTML tags: <br> <a> <small> <b> <i> <s> <sup> <sub> <u> <spoiler> <ul> <ol> <li>
To prove you are not a spam bot, please type "odd" in the box below (case sensitive):
© Matthew Scroggs 2019