Permutations And Combinations

Question
CBSEENMA11014267

In how many ways can the letters of the word ‘PERMUTATIONS’ be arranged if the:
(i) words start with P and end with S?
(ii) vowels are all together ?
(iii) there are always 4 letters between P and S?

Solution

Solution not provided.
Ans. (i) fraction numerator 10 factorial over denominator 2 factorial end fraction
       (ii) fraction numerator 8 space factorial over denominator 2 space factorial end fraction cross times 5 space factorial
       (iii) 14 cross times fraction numerator 10 factorial over denominator space 2 factorial end fraction space or space 7 space cross times space 10 factorial

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Some More Questions From Permutations and Combinations Chapter

Determine K, so that K + 2, 4K – 6 and 3K – 2 are three consecutive terms of an A.P.