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Verify that ""^nCr= frac (n)(r) "^(n-1)C...

Verify that `""^nC_r= frac (n)(r) "^(n-1)C_(r-1)` and hence prove that `"^nC_r= (n!)/(r!(n-r)!)` .

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MODERN PUBLICATION-PERMUTATIONS AND COMBINATIONS-EXERCISE
  1. Show that ((n+1)(n+2)(n+3)...... (n+r))/(r!) is a whole number.

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  2. Prove that "^(n-1)C3+ ^(n-1)C4 > ^nC3 if n >7.

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  3. Verify that ""^nCr= frac (n)(r) "^(n-1)C(r-1) and hence prove that "^n...

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  4. Find n if ""^nC4 , ""^nC5 and ""^nC6 are in A.P.

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  5. In how many ways can 5 sportsmen be selected from a group of 10 ?

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  6. How many selections of 4 books can be made from 8 different-books ?

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  7. A committee of 2 boys is to be selected from 4 boys. In how many ways ...

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  8. In how many ways can a committee be selected from 15 persons if the co...

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  9. In how many ways can a committee be selected from 15 persons if the co...

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  10. Sudha wants to choose any 9 stamps from a set of 11 different stamps. ...

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  11. How many lines can be drawn through 6 points on a circle ?

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  12. How many triangles can be drawn through n points on a circle ?

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  13. A polygon has 44 diagonals, find the number of its sides.

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  14. Find the number of diagonals of a : pentagon .

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  15. Find the number of diagonals of a : octagon .

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  16. If there are 12 persons in a party, and if each two of them shake hand...

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  17. In a student's reunion meeting in a school, 16 students show up. Each ...

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  18. How many different committees, each consisting of 3 girls and 2 boys c...

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  19. In how many ways can a team of 3 boys and 3 girls be selected from 5 b...

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  20. Find the number of ways of selecting 9 balls from 6 red balls, 5 white...

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