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

Show that `(.^(4n)C_(2n))/(.^(2n)C_(n))=(1.3.5......(4n-1))/({1.3.5......(2n-1)}^(2))`.

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Prove that , .^(2n)C_(n)=2^(n)(1.3.5...(2n-1))/(lfloorn)

If (1+x)^(n)=C_(0)+C_(1)+x+C_(2)x^(2)+...+C_(n) x^(n) Show that C_(1)^(2)+2*C_(2)^(2)+3*C_(3)^(2)....+n*C_(n)^(2)=((2n-1)!)/([(n-1)!]^(2))

Prove that .^(2n)P_(n)={1.3.5.....(2n-1)}.2n

Prove that .^(n)C_(1) + 2 xx .^(n)C_(2) + 3 xx .^(n)C_(3) + "…." + n xx .^(n)C_(n) = n2^(n-1) . Hence, prove that .^(n)C_(1).(.^(n)C_(2))^(2).(.^(n)C_(3))^(3)"......."(.^(n)C_(n))^(n) le ((2^(n))/(n+1))^(.^(n+1)C_(2)) AA n in N .

Prove that (2n!)/(n!)={1.3.5.....(2n-1)}2^n

Find the sum of the series .^(n)C_(0)+2.^(n)C_(1)x+3.^(n)C_(2)x^(2)+....+(n+1).^(n)C_(n)x^(n) and hence show that , .^(n)C_(0)+2.^(n)C_(1)x+3.^(n)C_(2)x^(2)+....+(n+1)^(n)C_(n)=(n+2)2^(n-1)

The value of (.^(n)C_(0))/(n)+(.^(n)C_(1))/(n+1)+(.^(n)C_(2))/(n+2)+"..."+(.^(n)C_(n))/(2n)

Prove that (.^(n)C_(1))/(2) + (.^(n)C_(3))/(4) + (.^(n)C_(5))/(6) + "…." = (2^(n) - 1)/(n+1) .

Show that , (2n)! =2^(n).n![1.3.5…(2n-1)].

If m=.^(n)C_(2) show that , .^(m)C_(2)=3.^(n+1)C_(4)

CHHAYA PUBLICATION-PERMUTATION AND COMBINATION -EXERCISE 7B ( Short Answer Type Questions )
  1. Prove that , .^(15)C(8)+^(15)C(9)-.^(15)C(6)-^(15)C(7)=0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  20. In an election there are 7 candidates and 4 members are to be elected...

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