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Prove that ""^(25)C(2) + overset(4)under...

Prove that `""^(25)C_(2) + overset(4)underset(r=0)(sum) ""^(29-r)C_(1)=435`

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435
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Prove that underset(rles)(underset(r=0)overset(s)(sum)underset(s=1)overset(n)(sum))""^(n)C_(s) ""^(s)C_(r)=3^(n)-1 .

Let V be the volume of the parallelopied formed by the vectors overset(to)(a) =a_(1) hat(i) +a_(2)hat(j) +a_(3)hat(k) , overset(to)(b) =b_(1)hat(i) +b_(2)hat(j) +b_(3)hat(k) " and " overset(to)(C) =c_(1)hat(i) +c_(2)hat(j) +c_(3)hat(k) If a_(r) , b_(r) , c_(r) where r=1,2,3 are non-negative real numbers and overset(3)underset(r=1)(Sigma) (a_(r)+b_(r)+c_(r))=3L. Show that V le L^(3)

Prove that ""^(n)C_r + ""^(n)C_(r-1) = ""^(n+1)C_r

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PREMIERS PUBLISHERS-COMBINATORICS AND MATHEMATICAL INDUCTION-PROBLEMS FOR PRACTICE (Choose the correct option for the following)
  1. Prove that ""^(25)C(2) + overset(4)underset(r=0)(sum) ""^(29-r)C(1)=43...

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  2. 0! Is :

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  3. If n different objects are to placed in m places then the number of wa...

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  4. There are 5 bulbs in a room. Each one of them can be operated independ...

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  5. If 7!/n!=7 then the value of n is:

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  6. If n! + (n-1)! =144, then the value of n is :

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  7. Prove ""^(n)P(r)=""^(n-1)P(r) +r. ""^(n-1)P(r-1)

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  8. ""^(7)C(3) + ""^(7)C(2)=""^(x)C(y) then x and y are:

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  9. If 5 parallel lines intersect another set of 4 , parallel lines (not p...

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  10. 1^(2) + 2^(2) + 3^(2) + …+ 10^(2) is :

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  11. If ""^(x^(2)-x)C(7)=""^(x^(2)-x)C(5) then x is :

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  12. A photographer wants to take a photo of 3 students out of 6 students ...

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  13. In 3 fingers, the number of ways five rings can be worn in...............

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  14. There are 8 points in a plane, no three of them are collinear .The num...

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  15. 10 students compete in a race. In how many ways first two prizes be g...

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  16. How many lines can be drawn given six points of which 3 are collinear?

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  17. Find the odd one out:

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  18. Among the following, find which one cannot be no. of digonals of a pol...

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  19. Find the correct statement:

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  20. Find the correct statement:

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  21. Find the incorrect statement:

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