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Find the number of ways in which the let...

Find the number of ways in which the letters of the word “ARRANGEMENT” can be arranged so that the two R’s and two A’s do not occur together.

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The number of ways in which the letters of the word ARRANGE be arranged so that (i) the two R's are never together, (ii) the two A's are together but not two R's. (iii) neither two A's nor two R's are together.

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MODERN PUBLICATION-PERMUTATIONS AND COMBINATIONS-EXERCISE
  1. Prove that 33! is divisible by 2^15.

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  2. If r is allowed to vary, find the value of r for which "^nCr is maximu...

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  3. Find the number of ways in which the letters of the word “ARRANGEMENT”...

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  4. How many words, with or without meaning, each of 2 vowels and 3 conson...

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  5. How many words, with or without meaning, can be formed using all the l...

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  6. In how many ways can the letters of the word ASSASSINATION be arranged...

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  7. In how many ways can the letters of the word 'ALGEBRA' can be arranged...

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  8. In how many ways can the letters of the word 'ALGEBRA' can be arranged...

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  9. In how many different ways can five boys and five girls form a circle ...

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  10. We wish to select 6 persons from 8, but if the person A is chosen, the...

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  11. Each of the six squares in the strip shown in the fig., is to be colou...

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  12. A mathematical club consists of 18 members. In how many Wars can the m...

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  13. How many arithmetic progressions with 10 terms are there whose first t...

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  14. There are 6 items in column A and 6 items in column B. A student is as...

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  15. A code word is to consist of two distinct English alphabets followed b...

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  16. How many 4-letter words, with or without meaning, can be formed out of...

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  17. Find the number of permutations of the letters of the words 'DADDY DID...

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  18. In how many different ways can the word ‘EATERAN EATER’ be arranged so...

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  19. Three married couples are to be seated in a row having six seats in a ...

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

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