Probability Question (1 Viewer)

[iheartOJ]

Hi
This is from the Cambridge 3U Ex 10F
"In how many ways can the letters of the word PROPORTIONALITY be arranged so that the vowels and consonants still occupy the same places"
Answer: 2721600

Thanks!

 

[HSC2014]

Vowels and consonants occupy the same positions in the word hence we only need to consider the number of arrangements inside the two groups themselves. I.e. (Permutations of vowels in group of vowels) x (Permutations of consonants in group of consonants)

 

[ymcaec]

Hi
This is from the Cambridge 3U Ex 10F
"In how many ways can the letters of the word PROPORTIONALITY be arranged so that the vowels and consonants still occupy the same places"
Answer: 2721600

Thanks!

We have 9 consonants and 6 vowels.
So we can arrange the consonants in 9! ways and vowels in 6! ways.
and remember there are duplicated letters !

 

[iheartOJ]

Ahh... I'm so silly!

Thanks ymcaec and HSC 2014!!!