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Prove that , .^(n)C(r)+3.^(n)C(r-1)+3.^(...

Prove that , `.^(n)C_(r)+3.^(n)C_(r-1)+3.^(n)C_(r-2)+^(n)C_(r-3)=^(n+3)C_(r)`

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Show that , (.^(n)C_(r)+^(n)C_(r-1))/(.^(n)C_(r-1)+^(n)C_(r-2))=(.^(n+1)p_(r))/(r.^(n+1)p_(r-1))

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Prove that .^(n)C_(0) - .^(n)C_(1) + .^(n)C_(2) - .^(n)C_(3) + "……" + (-1)^(r) .^(n)C_(r) + "……" = (-1)^(r ) xx .^(n-1)C_(r ) .

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If n is a positive integer then using the indentiy (1+x)^(n)=(1+x)^(3)(1+x)^(n-3) , prove that ""^(n)C_(r)=""^(n-2)C_(r)+3*""^(n-3)C_(r-1)*""^(n-3)C_(r-2)+""^(n-3)C_(r-3)

CHHAYA PUBLICATION-PERMUTATION AND COMBINATION -EXERCISE 7B ( Short Answer Type Questions )
  1. Prove that , .^(45)C(8)+sum(r=1)^(7).^(52-r)C(7)+sum(k=1)^(5).^(57-K)C...

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  2. Prove that , .^(15)C(8)+^(15)C(9)-.^(15)C(6)-^(15)C(7)=0

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  3. Prove that , .^(n)C(r)+3.^(n)C(r-1)+3.^(n)C(r-2)+^(n)C(r-3)=^(n+3)C(r)

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  4. Show that (.^(4n)C(2n))/(.^(2n)C(n))=(1.3.5......(4n-1))/({1.3.5........

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  5. If .^(n)C(r-1)=36,.^(n)C(r)=84and.^(n)C(r+1)=126 find n and r .

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  6. If (.^(n)C(r-1))/(a)=(.^(n)C(r))/(b)=(.^(n)C(r+1))/(c) n=(ab+2ac...

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  7. If the number of permutations of n different things taken r at time be...

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  8. For n in N , Prove that (n+1)[n!n+(n-1)!(2n-1)+(n-2)!(n-1)]=(n+2)!

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  9. Evaluate : .^(20)C(5)+sum(j=2)^(5).^(25-j)C(4)

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  10. If .^(n)C(1),^(n)C(2)and^(n)C(3) are in A.P ., find n .

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  11. Solve : ((2x+1)!)/((x+2)!)xx((x-1)!)/((2x-1)!)=(3)/(5),( x in N N)

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  12. Prove that if ngt7 then .^(n-1)C(3)+.^(n-1)C(4)gt^(n)C(3)

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  13. How many different triangles can be formed by joining the angular poi...

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  14. How many words each consisting of five different letters can be formed...

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  15. find the number of different words that can be formed from 12 consonan...

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  16. A person has got 15 acquaintances of whom 10 are relatives . In how ma...

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  17. In how many different ways can 9 men be selected from 15 men so as to ...

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  18. In how many ways can a committee of a 3 ladies and 4 gentlemen be appo...

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  19. m men and n women are to be seated in a row that no two women sit tog...

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  20. Eight prizes are to be distributed by a lottery . The first participa...

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