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Find the number of arrangemements of the...

Find the number of arrangemements of the letters of the word INDEPEDENCE. In how many of these arrangments ,
(i) DO the words start with P.
(ii) DO all the vowels always occur together .
(iii) Do the vowels never occur togather
(Iv) do the words begin with I and end in P?

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The correct Answer is:
(i) 138600, (ii) 16800, (iii) 1646400, (iv) 12600
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KUMAR PRAKASHAN-PERMUTATIONS AND COMBINATIONS-TEXTBOOK ILLUSTRATIONS FOR PRACTICE WORK
  1. Evaluate : (i) 5 ! (ii) 7 ! (iii) 7 ! - 5 !

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  2. Compute (i) (7!)/(5!) (ii) (12!)/((10!)(2!)

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  3. Evaluate (n!)/(r!(n-r)!), when n = 5, r = 2.

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  4. If (1)/(8!)+(1)/(9!)=(x)/(10!), find x.

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  5. Find the number of permutations of the letters of the word ALLAHABAD.

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  6. How many 4-digit numbers can be formed by using the digits 1 to 9 if ...

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  7. How many numbers lying between 100 and 1000 can be formed with the di...

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  8. Find the value of n such that, ""^(n)P(2)=30

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  9. Find r, if 5""^(4)P(r)=6""^(5)P(r-1)

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  10. Find the number of different 8-letter arrangements that can be made f...

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  11. In how many ways can 4 red, 3 yellow and 2 green discs be arranged in...

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  12. Find the number of arrangemements of the letters of the word INDEPEDEN...

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  13. If ""^nc9= ^nc17.

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  14. A committee of 3 persons is to be constituted from a group of 2 men an...

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  15. What is the number of ways of choosing 4 cards from a pack of 52 play...

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  16. How many words, with or without meaning, each of 3 vowels and 2 conso...

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  17. A group consists of 4 girls and 7 boys. In how many ways can a team of...

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  18. Find the number of words with or without meaning which can be made us...

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  19. How many numbers greater than 1000000 can be formed by using the digi...

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  20. In how many ways can 5 girls and 3 boys be seated in a row so that no...

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