Suppose that a “word” is any string of six letters. Repeated letters are allowed. For our...

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Advance Math

Suppose that a “word” is any string of six letters. Repeatedletters are allowed. For our purposes, vowels are the letters a, e,i, o, and u. a) How many words are there? b) How many words beginwith a vowel? c) How many words begin with a vowel and end with avowel? d) How many words have no vowels? e) How many words haveexactly one vowel?
A professor teaching a Discrete Math course gives a multiplechoice quiz that has six
questions, each with four possible responses: a, b, c, d. What isthe minimum number of students that
must be in the professor’s class in order to guarantee that atleast three answer sheets must be identical?
(Assume that no answers are left blank.)

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Question 1 a Number of words 266 since each letter can be selected from one of the 26 characters az b Number of words being with vowel 5 265 since the first place must be filled with a vowel which are 5 aeiou rest 5 places can be filled by any alphabet c Number of words being with vowel See Answer

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