Answer:
66361680
Explanation:
Case 1 : With no vowels
No, of vowels = 5
Remaining alphabets = 26-5 =21
No. of letters for for a word to be formed = 6
So, No. of ways of length 6 formed with no vowels from the 26 letters without repetition:
=
=
Case 2 : With vowels at first and last place
No. of vowels = 5
No. of ways of putting 2 vowels on first and last place of 6 letter word with no repetition =
Remaining alphabets = 26-5 =21
So, No. of ways of filling 4 places without repetition with no vowels :
=
=
So, No. of ways of length 6 formed with both vowels from the 26 letters without repetition:
Case 3 : with vowel at first place
No. of vowels = 5
No. of ways of putting 1 vowels on first place of 6 letter word with no repetition =
Remaining alphabets = 26-5 =21
So, No. of ways of filling 5 places without repetition with no vowels :
=
=
So, No. of ways of length 6 formed with vowel at first place from the 26 letters without repetition:
Case 4: with vowel at last place
No. of vowels = 5
No. of ways of putting 1 vowels on last place of 6 letter word with no repetition =
Remaining alphabets = 26-5 =21
So, No. of ways of filling 5 places without repetition with no vowels :
=
=
So, No. of ways of length 6 formed with vowel at last place from the 26 letters without repetition:
So, total no. of ways of length 6 formed from the 26 letters without repetition are there where the vowels (a,e,i,o,u) may only appear in the first or/and last positions (possibly neither):
= 39070080+2872800+12209400+12209400
=66361680
Hence total no. of ways of length 6 formed from the 26 letters without repetition are there where the vowels (a,e,i,o,u) may only appear in the first or/and last positions (possibly neither) is 66361680