Consider the word "FRIENDS". (a) In how many different ways can the 7 letters of “FRIENDS” be arranged? (b) In how many

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Consider The Word Friends A In How Many Different Ways Can The 7 Letters Of Friends Be Arranged B In How Many 1 (136.37 KiB) Viewed 51 times

Consider the word "FRIENDS". (a) In how many different ways can the 7 letters of “FRIENDS” be arranged? (b) In how many different ways can these 7 letters be arranged, if the first letter and the last letter must be vowels? [3] [3] (c) In how many different ways can these 7 letters be arranged, if the first letter and the last letter must be consonants? [3] (d) (i) How many n-letter words can be formed from these 7 letters if letters may be re- peated? [3] (ii) Write down the (ordinary) generating function for the number an of n-letter words calculated above and express it in terms of elementary functions. [3] (e) How many 16-letter words are there consisting of 5 Es, 2 Is and 9 Ps? [3] (f) How many 16-letter words are there consisting of 5 Es, 2 Is and 9 consonants from the set {F, R, N, D, S}? [4]