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?

 

[msk]

i Think it should be 6!

 

[ahmed t]

10!/5!

 

[usman]

You can arrange 10 different objects in 10! ways. In the given question, although 5 of the objects have to be placed in a specific order, 5 such objects could be arranged among themselves in 5! ways with no restrictions. Hence the given problem can be solved in 10!/5! = 30240 ways

 

[soumayya]

^A^E^I^O^U^
where ^ are possible places for placing a consonant...
there are 5 consonants...and 6 places...
so i would go for 6P5 =720

hpe zat hlps...

 

[anzaar]

like soumayya elaborated
^A^E^I^O^U^
There are six positions and five letters to be adjusted.
five positions (vowel letters)have been fixed in specific order. you have left 6 positions with 5 letters to adjust.
this can b done starting 1st position till letters are finished and last position left
and starting filling from 2nd position till last one. hence your ans is.
5! +5!
or 2*(5!)= 240 ways

 

[princesszahra]

You can arrange 10 different objects in 10! ways. In the given question, although 5 of the objects have to be placed in a specific order, 5 such objects could be arranged among themselves in 5! ways with no restrictions. Hence the given problem can be solved in 10!/5! = 30240 ways

correct!

 

[ahmed t]

guys we already established the anser as 10!/5! earlier in the forum by me and usman and that is the correct anser so thnx for the replys but MW24595 got the anser