Respuesta :
Answer:
66361680
Step-by-step 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:
= [tex]21 \times 20 \times 19 \times 18 \times 17 \times 16[/tex]
= [tex]39070080[/tex]
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 = [tex]5 \times 4 = 20[/tex]
Remaining alphabets = 26-5 =21
So, No. of ways of filling 4 places without repetition with no vowels :
= [tex]21 \times 20\times 19 \times 18 [/tex]
= [tex]143640 [/tex]
So, No. of ways of length 6 formed with both vowels from the 26 letters without repetition: [tex]143640 \times 20 =2872800[/tex]
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 = [tex]5 [/tex]
Remaining alphabets = 26-5 =21
So, No. of ways of filling 5 places without repetition with no vowels :
= [tex]21 \times 20\times 19 \times 18 \times 17 [/tex]
= [tex]2441880 [/tex]
So, No. of ways of length 6 formed with vowel at first place from the 26 letters without repetition: [tex]2441880 \times 5 =12209400[/tex]
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 = [tex]5 [/tex]
Remaining alphabets = 26-5 =21
So, No. of ways of filling 5 places without repetition with no vowels :
= [tex]21 \times 20\times 19 \times 18 \times 17 [/tex]
= [tex]2441880 [/tex]
So, No. of ways of length 6 formed with vowel at last place from the 26 letters without repetition: [tex]2441880 \times 5 =12209400[/tex]
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
