3. How many strings of eight English letters are there a) that contain no vowels, if letters can be repeated? b) that contain no vowels, if letters cannot be repeated? c) that start with a vowel, if letters can be repeated? d) that start with a vowel, if letters cannot be repeated? e) that contain at least one vowel, if letters can be repeated? f ) that contain exactly one vowe

First of all we know there are Twenty six (26) letters in the alphabet.

Five (5) vowels

Twenty one (21) consonants

a) that contain no vowels, if letters can be repeated?

No vowels = all consonants

Hence,

21⁸ = 37,822,859,361letters

b) that contain no vowels, if letters cannot be repeated?

Hence,

21×20×19×18×17×16×15×14 = 8,204,716,800letters

c) that start with a vowel, if letters can be repeated?

Hence,

5×26⁷ = 40,159,050,880letters

d) that start with a vowel, if letters cannot be repeated?

Hence,

5×25×24×23×22×21×20×19 = 12,113,640,000letters

e) that contain at least one vowel, if letters can be repeated?

Hence,

26⁸-21⁸ = 171,004,205,215letters

f) that contain exactly one vowel, if letters can be repeated?

Hence,

8×(5×21⁷) = 72,043,541,640letters

the bazaar because it represents the inaccessible land of freedom to the narrator. mangan’s sister because she represents domesticity and routine to the narrator. the marketplace because it represents the suburban lifestyle to the narrator. the church because it represents spiritual healing and renewal to the narrator.

b is the answer