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Prove that ""^(25)C(4)+ Sigma(r=0)^(4...

Prove that
`""^(25)C_(4)+ Sigma_(r=0)^(4) ""^((29-r))C_(3)=""^(30)C_(4)`

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The correct Answer is:
`=""^(29)C_(4)+""^(29)C_(3)=""^(30)C_(4)`
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VIKRAM PUBLICATION ( ANDHRA PUBLICATION)-PERMUTATIONS AND COMBINATIONS-TAXTUAL EXERCISES
  1. Prove that ""^(25)C(4)+ Sigma(r=0)^(4) ""^((29-r))C(3)=""^(30)C(4)

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  2. If ""^(n)P(7)=42. ""^(n)P(5). find n.

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  3. If ""^((n+1))P(5): ""^(n)P(6)=2:7, find

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  4. If ""^(12)P(5)+5. ""^(12)P(4)=""^(13)P(r), find r.

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  5. If ""^(18)P((r-1)):""^(17)P((r-1))=9:7, find r.

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  6. A man has 4 sons and there are 5 schools within his reach. In how many...

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  7. If there are 25 railway stations on a railway line, how many types of ...

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  8. In a class there are 30 students. On the New year day, every student p...

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  9. Find the number of ways of arranging the letters of the word TRIANGLE ...

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  10. Find the number of numbers that are greater than 4000 which can be for...

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  11. Find the number of ways of arranging the letters of the word MONDAY so...

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  12. Find the number of ways of arranging 5 different mathematics books, 4 ...

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  13. Find the number of 5 letter words that can be formed using the letters...

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  14. Find the number of ways of seating 10 students A(1), A(2)…..A(10) in a...

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  15. Find the number of ways in which 5 red balls, 4 black balls of differe...

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  16. Find the number of ways in which 5 red balls, 4 black balls of differe...

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  17. Find the number of 4 - digit numbers that can be formed using the digi...

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  18. If the letters of the word BRING are permuted in all possible ways and...

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  19. Find the sum of all 4 digited numbers that can be formed using the dig...

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  20. There are 9 objects and 9 boxes. Out of 9 objects, 5 cannot fit in thr...

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  21. Find the number of 4- digited numbers that can be formed using the dig...

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