probability (1 Viewer)

[Pocatello]

If all the letters making up the word Wollongong are placed in to a hat and drawn out, what is the probability of:
a) The word beginning with an 'o'
b) The word having no two identical letters in a row
c) At least one 'l' placed between the 'g''s


Thanks

 

[damo676767]

If all the letters making up the word Wollongong are placed in to a hat and drawn out, what is the probability of:
a) The word beginning with an 'o'
b) The word having no two identical letters in a row
c) At least one 'l' placed between the 'g''s


Thanks

interesting

part a)
3/10


part b)
prob of l's in a row
9/¹⁰C₂
1/5

prob of g's in a row
9/¹⁰C₂
1/5

prob of n's in a row
9/¹⁰C₂
1/5

prob of o's in a row
71/¹⁰C₃
71/120


prob of l's and g's
1/5 * 1/5
1/25

prob of l's and n's
1/5 * 1/5
1/25

prob of l's and 0's
1/5 * 7/120
7/600

prob of g's and n's
1/5 * 1/5
1/25

prob of g's and o's
1/5 * 7/120
1/600

prob of n's and o's
1/5 * 1/120
1/600

prob of l's and g's and n's
1/5 * 1/5 * 1/5
1/125

prob of l's and g's and o's
1/5 * 1/5 * 7/120
7/3000

prob of l's and o's and n's
1/5 * 1/5 * 7/120
7/3000

prob of o's and g's and n's
1/5 * 1/5 * 7/120
7/3000

prob of all
1/5 * 1/5 * 1/5 * 7/120
7/15000


ther fore prob of none
p = 1 - (1/5 + 1/5 + 1/5 + 7/120 - 1/25 - 1/25 - 7/600 - 1/25 - 1/600 - 1/600 - 1/125 - 7/3000 - 7/3000 - 7/3000 - 7/15000)
= 3691/7500

ther must be an eaier way to do it

part c)
i'l sleep on it

 

[Pocatello]

What do you think?

a) (9!/3!2!2!2!)/(10!/3!2!2!2!)

 

[hereSIR]

This can't be correct, since you are ignoring the cases where only two of the three o's occur together

 

[Affinity]

You dig up a stale thread just for this!

 

[SoulSearcher]

This can't be correct, since you are ignoring the cases where only two of the three o's occur together