Exercise 4. Let C be the set of 26 letters of the alphabet, in lowercase. Let A

Question

Exercise 4. Let C be the set of 26 letters of the alphabet, in lowercase. Let A be the set of six-long letter strings, in which letters may repeat. This set, and the subsets listed below, can be counted using trees. You may give your answer as a product, to indicate how you found the formula. (A) A itself. (B) The subset B C A of all strings in which no letter appears more than (C) The subset C in which the letters a, e, i, o, u do not appear. once. (D) The subset D in which the second and fourth letters agree and no other letters agree. (E) The subset E in which no two successive letters agree (that is, the first letter is not the second, the second is not the third, etc)

Explanation / Answer

a) for each letter there are 26 choices ; therefore number of ways =26*26*26*26*26*26

b) for first letter has 26 ; second 25 ; third 24 .. and so on choices, hence number of ways=26*25*24*23*22*21

c)

for we need to choose from remaing 21 alphabets ; numebr of ways =21*21*21*21*21*21

d) here we need to choose for only 2 nd letter ; the fourth has to be same as second so number of choices for that =1

hence number of ways =26*25*24*23*22

e)for first there are 26 choice ; for second 25 except that has been selected in first; for third 25 except that has been selected in second, and so on,,,

hen ce number of ways =26*25*25*25*25*25

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