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If .^(n)C(12) = .^(n)C(9) " find " .^(2...

If `.^(n)C_(12) = .^(n)C_(9) " find " .^(21) C_(n)`

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If .^(n)C_(8)=^(n)C_(6) , then find .^(n)C_(2) .

If ""^(n)C_(4)=""^(n)C_(6) find ""^(12)C_(n) .

If ""^(n)C_(8)=""^(n)C_(2) , find ""^(n)C_(2) .

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

If ""^(n)C_(9)=""^(n)C_(8) , find ""^(n)C_(17) .

Find the sum 1.^(n)C_(0) + 3 .^(n)C_(1) + 5.^(n)C_(2) + "….." + (2n+1).^(n)C_(n) .

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

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) .

In ""_(n)C_(12)=""_(n)C_(8) then n=

PREMIERS PUBLISHERS-COMBINATORICS AND MATHEMATICAL INDUCTION-EXERCISE 4.3
  1. If .^(n)C(12) = .^(n)C(9) " find " .^(21) C(n)

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  2. If .^(15)C(2r-1) = .^(15)C(2r + 4) " find " r

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  3. If .^(n)P(r) = 720 . " If " .^(n)C(r) = 120 " find " n , r

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  4. Prove that .^(15)C(3) + 2 xx .^(15)C(4) + .^(15)C(5) = .^(17)C(5)

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  5. Prove that .^(35)C(5) + sum(r=0)^(4^((39-r))) C(4) = .^(40)C(5)

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  6. If .^(n+2) C(8) : ^((n-2)) P(4) = 57: 16 , find the value of n.

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  7. Prove that .^(2n)C(n) = ( 2^(n) xx 1 xx 3 xx …(2n-1))/(n!)

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  8. Prove that if 1 le r le n " then " n xx^((n-1))C(r-1)= (n-r+1).^(n)...

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  9. A Kabaddi coach has 14 players ready to play. How many different...

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  10. There are 15 persons in a party and if each 2 of then shakes hands w...

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  11. How many chords can be drawn through 20 points on a circle ?

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  12. In a parking lot one hundred one year old cars, are parked. Out of t...

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  13. How many ways can a team of 3 boys, 2 girls and 1 transgender be se...

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  14. Find the total number of subsets of a set with . (i) 4 elements (...

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  15. Find the total number of subsets of a set with . (i) 4 elements (...

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  16. Find the total number of subsets of a set with . (i) 4 elements (...

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  17. A trust has 25 members . (i) How many ways 3 officers can be sel...

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  18. A trust has 25 members . (i) How many ways 3 officers can be sel...

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  19. How many ways a committee of six persons from 10 persons can be chosen...

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  20. How many different selections of 5 books can be made from 12 differe...

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