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Prove that ""^nCr+4^nC(r-1)+6^(n)C(r-2)+...

Prove that `""^nC_r+4^nC_(r-1)+6^(n)C_(r-2)+4^nC_(r-3)+^nC_(r-4)=^(n+4)C_r`

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A N EXCEL PUBLICATION-PERMUTATIONS AND COMBINATIONS-QUESTION BANK
  1. If (c(n,r))/(c(n,r+1))=1/2 and (c(n,r+1))/(c(n,r+2))=2/3, prove that ...

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  2. Prove that ""^nCr+^nC(r-1)=^(n+1)Cr

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  3. Prove that ""^nCr+4^nC(r-1)+6^(n)C(r-2)+4^nC(r-3)+^nC(r-4)=^(n+4)Cr

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  4. Find the value of 5!

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  5. If (n!)/((n-2)!)=56, find the value of n

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  6. Find the value of ""^6C2

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  7. If ""^nC14=^nC20 find the values of ""^nC28 and ""^nC32

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  8. In how many ways can a cricket team of 11 of players be selected from ...

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  9. A cricket team consists of 15 players, out of it 5 are bowlers. In how...

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  10. A cricket team consists of 15 players, out of it 5 are bowlers. In how...

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  11. Determine the number of 5 card combinations out of a deck of 52 cards ...

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  12. From a deck of 52 cards, 5 cards combination is taken out Find the nu...

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  13. From a deck of 52 cards, 5 cards combination is taken out Find the nu...

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  14. There are 8 men and 5 women How many committees can be formed if it c...

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  15. There are 8 men and 5 women How many committees of 5 men and 3 women ...

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  16. There are 8 men and 5 women. How many committees consists of 5 men and...

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  17. Consider a group of 5 boys and 4 girls In how many ways 3 boys can be ...

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  18. Consider a group of 5 boys and 4 girls In how many ways 3 girls can be...

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  19. In how many different ways can a team of 3 boys and 3 girls be selecte...

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  20. In an examination a question paper consists of' 12 questions divided i...

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