mscroggs.co.uk
mscroggs.co.uk

subscribe

Blog

Countdown probability

 2014-04-06 
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
090
180
270
360.000546
450.019724
540.076895
630.051417
720.005662
810.000033
900
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
Big Internet Math-Off stickers 2019
World Cup stickers 2018, pt. 3

Comments

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 "pmuj" backwards in the box below (case sensitive):

Archive

Show me a random blog post
 2021 

May 2021

Close encounters of the second kind

Jan 2021

Christmas (2020) is over
 2020 
▼ show ▼
 2019 
▼ show ▼
 2018 
▼ show ▼
 2017 
▼ show ▼
 2016 
▼ show ▼
 2015 
▼ show ▼
 2014 
▼ show ▼
 2013 
▼ show ▼
 2012 
▼ show ▼

Tags

game of life probability advent calendar programming rhombicuboctahedron manchester dragon curves sorting stickers chebyshev statistics logs puzzles world cup noughts and crosses dates golden spiral national lottery determinants matrix of cofactors inverse matrices polynomials signorini conditions european cup mathslogicbot misleading statistics tmip approximation pascal's triangle binary interpolation data london underground folding tube maps computational complexity bodmas guest posts finite element method a gamut of games harriss spiral quadrilaterals rugby oeis the aperiodical news estimation folding paper manchester science festival bubble bobble cambridge speed captain scarlet christmas card ucl matrix of minors logic menace propositional calculus graph theory draughts ternary reddit inline code accuracy phd fractals raspberry pi realhats javascript mathsjam chess mathsteroids light wool radio 4 sobolev spaces boundary element methods numbers recursion map projections convergence pac-man php platonic solids curvature go nine men's morris reuleaux polygons pythagoras pizza cutting pi martin gardner sound bempp people maths golden ratio talking maths in public matt parker hats dataset flexagons craft games pi approximation day hannah fry trigonometry chalkdust magazine big internet math-off hexapawn machine learning royal institution tennis error bars frobel matrix multiplication final fantasy twitter simultaneous equations books preconditioning matrices london countdown palindromes christmas data visualisation triangles video games braiding stirling numbers geometry geogebra electromagnetic field exponential growth plastic ratio coins asteroids weak imposition graphs gerry anderson latex football royal baby python gaussian elimination game show probability cross stitch sport weather station numerical analysis squares arithmetic wave scattering

Archive

Show me a random blog post
▼ show ▼
© Matthew Scroggs 2012–2021