Question

The number of ways to order (in line) the 26 letters of English alphabet so that no two
vowels (a, e, i, o, and u) occur consecutively is?​

Answer 1

Answer:

instead of a,e,i,o,u. all alphabets

Answer 2

We have total no. of alphabets = 26

No.of vowels = 5

No. of constants = 21

Required condition is no two vowels should be together when all 26 alphabets are arranged.

To attain this condition vowels are to be arranged alternatively in between consonants.

when first all 21 consonants are placed we will have 22 places to arrange vowels around those consonants.

_b _ c _ d _ f _ h _ j _ k _ l _ m _ n _ p _ q _ r _ s _ t _ v _ w _ x _ y _ z _

we can arrange these vowels in in 5 places out of 22 places in ,

$22_{P_{5} } ways$ .

And those 21 consonants can be arranged among themselves in 21 ! ways.

∴Total the no. of ways in which we can have arrangements for required condition is, $22_{P_{5} } *21 !$

HOPE THIS HELPS YOU .!!