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How many permutations of the letters A B C D E F G H consist of string DEF?
Ans: It is the dilemma of finding number of words that can be formed along with the given 8 letters in which DEF come together in that order. There will be six letters to be utilized to form words: A, B, C, DEF, G, H. They can be permuted in 6! = 720 ways. So required number of words is 720.
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Let a 0 , a 1 ::: be the series recursively defined by a 0 = 1, and an = 3 + a n-1 for n ≥ 1. (a) Compute a 1 , a 2 , a 3 and a 4 . (b) Compute a formula for an, n ≥ 0.
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