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

we would need to be able to read the passage in question to determine which factor allowed david believe he could defeat goliath. post the passage, and i'd love to out.

the answer is not b, and i don't think its a, so i choose either man's identity is found within the traditions of his ancestors   or language is a powerful tool, tell me if i was wrong or right by the way