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

Prove that ` .^(35)C_(5) + sum_(r=0)^(4^((39-r))) C_(4) = .^(40)C_(5)`

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`=""^(40)C_(5)=RHS`
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FULL MARKS-COMBINATORICS AND MATHEMATICAL INDUCTION-EXERCISE 4.3
  1. If .^(n)P(r) = 720 . " If " .^(n)C(r) = 120 " find " n , r

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

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

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

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

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

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  7. (i) A kabaddi coach has 14 players ready to play. How many different t...

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

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

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

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

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  12. There are 5 teachers and 20 students. Out of them a committee of 2 tea...

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  13. In an examination a student has a answer 5 questions, out of 9 quest...

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  14. Determine the number of 5 card combinations out of a deck of 52 car...

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  15. Find the number of ways of forming a committee of 5 members out of...

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

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  17. 7 relatives of a man comprises 4 ladies and 3 gentlemen, his wife also...

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  18. A box contains two white balls, three black balls and four balls. In...

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  19. Find the number of strings of 4 letters that can be formed with the le...

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  20. How many triangle can be formed by joining 15 points on the plane, in ...

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