Consider the collection of 5-letter strings using the 26-letter English alphabet. Five of these letters, A...

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Consider the collection of 5-letter strings using the 26-letter English alphabet. Five of these letters, A E I O U, are called vowels; the remaining letters are called consonants. (a) How many such strings are there? (b) How many strings begin and end with a vowel? (c) How many strings contain exactly one vowel? (d) How many strings contain two consecutive E's or two consecutive O's but no other vowels? (e) How many strings contain at least two vowels? Consider the collection of 5-letter strings using the 26-letter English alphabet. Five of these letters, A E I O U, are called vowels; the remaining letters are called consonants. (a) How many such strings are there? (b) How many strings begin and end with a vowel? (c) How many strings contain exactly one vowel? (d) How many strings contain two consecutive E's or two consecutive O's but no other vowels? (e) How many strings contain at least two vowels?