Mathematics

[MW24595]

Salaam,
I came across this question while doing a sample Question Paper and have gotten stuck rather badly.
It would be much appreciated if anyone could offer help or a solution of sorts. Thank You.
It says:

In how many ways can the ten letters of the word GELATINOUS be arranged in a line so that the vowels are in alphabetical order (not necessarily together) when read from left to right?

 

[ahmed t]

im not sure but i think if u treat all the vowels as the same letter it might give u the correct ans.
then it would be 10!/5!

 

[MW24595]

Hmm...Incidentally the final answer is right, but I don't understand how you got 10!/5! ? Please explain.

 

[msk]

10! is the possibility of all the letter we divide by 5! because vowels are included in the ten digit and the possibilty if 5!....so 10!/5! ...!

 

[ahmed t]

well if u treat all the vowels as one letter u do not include the order of the vowels,
as there is only one order which is A E I O U
the rest of the letters can be rearanged in many ways 10!
so we divide by the number of vowels 5!
i cant explain much more than that sorry