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

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

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

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

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

Prove that (.^(2n)C_0)^2-(.^(2n)C_1)^2+(.^(2n)C_2)^2-..+(.^(2n)C_(2n))^2 = (-1)^n.^(2n)C_n .

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

Show that the middle term in the expansion of (x+1)^(2n) is (1.3.5.....(2n-1))/(n!) 2^n.x^n .

Prove that, lim_(ntooo)(3.5+5.7+7.9+.......+(2n+1)(2n+3))/(n^(3))=(4)/(3)

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

Prove that .^(n)C_(0) +5 xx .^(n)C_(1) + 9 xx .^(n)C_(2) + "…." + (4n+1) xx .^(n)C_(n) = (2n+1) 2^(n) .

Prove that , (x^(n))/(n!)+(x^(n-1).a)/((n-1)!1!)+(x^(n-2).a^(2))/((n-2)!2!)+(x^(n-3).a^(3))/((n-3)!3!)+.......(a^(n))/(n!)=(x+a)^(n)/(n!)

CHHAYA PUBLICATION-PERMUTATION AND COMBINATION -EXERCISE 7A ( Very Short Answer Type Questions )
  1. If .^(n+1)P(4):^(n-1)P(3)=72:5, find n.

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  2. If 16.^(15)P(n)=13.^(16)P(n), find n.

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

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  4. If .^(9)P(5)+5.^(9)P(4)=^(10)P(r), find r.

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  5. In how many different ways can 4 prizes be distributed among 10 studen...

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  6. On entering a certain town ,4 travellers find that there are 5 hotels ...

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  7. 12 ferry - steamers ply between Chandpal Ghat and Botanical Garden . I...

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  8. There are 12 stations on a certain railway line . How many different k...

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  9. How many different permutations can be made by taking all the letters ...

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  10. Find the number of ways in which the letters of the word DRAUGHT can b...

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  11. How many numbers each lying between 100 and 1000 can be formed with th...

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  12. Find the number of different perpmutations that can be made out of the...

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  13. Find the number of different perpmutations that can be made out of the...

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  14. Find the number of different perpmutations that can be made out of the...

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  15. Find the number of different perpmutations that can be made out of the...

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  16. Find the number of different perpmutations that can be made out of the...

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  17. In how many ways can the letters of the name Gavaskar be arranged so t...

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  18. In how many ways can the results of 3 successive football matches be d...

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  19. In how many ways can a person post 5 letters in 4 letters boxes ?

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  20. In how many ways four prizes - one for recitation , one for sports , o...

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