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Prove that ""^(10)C(2)+2xx^(10)C(3)+^(10...

Prove that `""^(10)C_(2)+2xx^(10)C_(3)+^(10)C_(4)=^(12)C_(4)`

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

Find the value of .^(20)C_(0) xx .^(13)C_(10) - .^(20)C_(1) xx .^(12)C_(9) + .^(20)C_(2) xx .^(11)C_(8) - "……" + .^(20)C_(10) .

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) .

Find the value of (.^(10)C_(10))+(.^(10)C_(0)+.^(10)C_(1))+(.^(10)C_(0)+.^(10)C_(1)+.^(10)C_(2))+"...."+(.^(10)C_(0)+.^(10)C_(1)+.^(10)C_(2)+"....." + .^(10)C_(9)) .

The value of .^(n)C_(0) xx .^(2n)C_(r) - .^(n)C_(1)xx.^(2n-2)C_(r)+.^(n)C_(2)xx.^(2n-4)C_(r)+"…." is equal to

If |{:(.^(9)C_(4),.^(9)C_(5),.^(10)C_(r)),(.^(10)C_(6 ),.^(10)C_(7),.^(11)C_(r+2)),(.^(11)C_(8),.^(11)C_(9),.^(12)C_(r+4)):}|=0 , then the value of r is equal to

FULL MARKS-COMBINATORICS AND MATHEMATICAL INDUCTION-ADDITIONAL QUESTIONS
  1. Prove that ""^(10)C(2)+2xx^(10)C(3)+^(10)C(4)=^(12)C(4)

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  2. If the letter of the word 'RACHIT' are arrenged in all possible ways a...

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  3. Count the number of positive integers greater than 6000 and less than ...

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  4. Find the number of integers greater than 7000 that can be formed with ...

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  5. How many words (with or without dictionary meaning ) can be made from ...

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  6. How many automobile license plates can be made, if each plate contains...

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  7. If (n!)/(3!(n-4)! and (n!)/(5!(n-5)! are in the ratio 5:3 find the val...

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  8. How many 3-digit even numbers can be made using the digits 1,2,3,4,6,7...

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  9. If ""^(n-1)P(3): ""^(n)P(4)=1:9 find n.

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  10. Out of 18 points in a plane, no three are in the same line except five...

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  11. We wish to select 6 person from 8 but , if the person A is choosen , t...

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  12. How many 3-digit numbers can be made using digit 1,2,3,4,6,7 if no dig...

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  13. Find the number of 4-digit numbers that can be formed using the digits...

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  14. Iff ""^(5)P(r)=""^(6)P(r-1) find r.

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  15. How many words, with or without meaning , can be made from the letters...

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  16. A group consists of 4 girls and 7 boys. In how many ways can a team of...

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  17. A committee of 6 is to be choosen from 10 men and 7 women so as to con...

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  18. Using the digits 1,2,3,4,5,6,7 a number of 4 different digits is forme...

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  19. If ""^(22)P(r+1):^(20)P(r+2)=11:52, find r.

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  20. If ""^(nP(r)=""^(n)P(r+1) and ""^(n)C(r)=""^(n)C(r-1) find n and r.

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  21. A committee of 7 peoples has to be formed from 9 men and 4 women . In ...

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