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

Archive

Show me a random blog post
 2020 

Jul 2020

Happy π+√3-4 Approximation Day!

May 2020

A surprising fact about quadrilaterals
Interesting tautologies

Mar 2020

Log-scaled axes

Feb 2020

PhD thesis, chapter ∞
PhD thesis, chapter 5
PhD thesis, chapter 4
PhD thesis, chapter 3
Inverting a matrix
PhD thesis, chapter 2

Jan 2020

PhD thesis, chapter 1
Gaussian elimination
Matrix multiplication
Christmas (2019) is over
 2019 
▼ show ▼
 2018 
▼ show ▼
 2017 
▼ show ▼
 2016 
▼ show ▼
 2015 
▼ show ▼
 2014 
▼ show ▼
 2013 
▼ show ▼
 2012 
▼ show ▼

Tags

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

Archive

Show me a random blog post
▼ show ▼
© Matthew Scroggs 2012–2020