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Find n if ""^(n)C(4)=""^(n)C(6)...

Find n if `""^(n)C_(4)=""^(n)C_(6)`

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To solve the problem where we need to find \( n \) such that \( \binom{n}{4} = \binom{n}{6} \), we can follow these steps: ### Step 1: Understand the relationship between combinations We know that if \( \binom{n}{x} = \binom{n}{y} \), then it holds that \( x + y = n \). ### Step 2: Identify \( x \) and \( y \) In our case, we have: - \( x = 4 \) ...
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Explore conceptually related problems

Find n, if ""^(n)C_(n-4)=5

If ""^(n)C_4= ""^(n)C_6, find n.

The arithmetic mean of ""^(n)C_(0),""^(n)C_(1),""^(n)C_(2), ..., ""^(n)C_(n) , is

The value of ""^(n)C_(n)+""^(n+1)C_(n)+""^(n+2)C_(n)+….+""^(n+k)C_(n) :

The least positive integer n for which ""^(n-1)C_(5)+""^(n-1)C_(6) lt ""^(n)C_(7) is

The expression ""^(n)C_(r)+4.""^(n)C_(r-1)+6.""^(n)C_(r-2)+4.""^(n)C_(r-3)+""^(n)C_(r-4)

If ([""^(n)C_(r) + 4*""^(n)C_(r+1) + 6*""^(n)C_(r+2)+ 4*""^(n)C_(r+3) + ""^(n)C_(r+4)])/([""^(n)C_(r) + 3. ""^(n)C_(r+1)+ 3*""^(n)C_(r+2) + ""^(n)C_(r +3)])=(n + lambda)/(r+lambda) the value of lambda is

Find the value of n: (i) .^(n)C_(10)=^(n)C_(16) (ii) .^(15)C_(n) =^(15)C_(n+3) (iii) .^(10)C_(n) =^(10)C_(n+2) (iv) .^(25)C_(3n) =.^(25)C_(n+1) (v) .^(n)C_(r) =.^(n)C_(r-2)

Find the following sums : (i) sumsum_(inej) ""^(n)C_(i).""^(n)C_(j) , (ii) sumsum_(0leiltjlen) ""^(n)C_(i).""^(n)C_(j) . (iii) sumsum_(0leiltjlen) ""^(n)C_(i).""^(n)C_(j) .

Find the sum sum_(r=1)^(n) r^(2) (""^(n)C_(r))/(""^(n)C_(r-1)) .

AAKASH INSTITUTE ENGLISH-PERMUTATIONS AND COMBINATIONS -Try Yourself
  1. Evaluate : ""^(75)C(73)

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  2. Evaluate : ""^(13)C(10)

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  3. Find n if ""^(n)C(4)=""^(n)C(6)

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  4. If ""^(n)C(10)=""^(n)C(13) , then find the value of ""^(n)C(2)

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  5. If ""^(15)C(x)=""^(15)C(x+3) , then find the value of X.

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  6. Find ""^(18)C(3)+^(18)C(2)

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  7. Verify that ""^(9)C(5)+""^(9)C(4)=""^(10)C(5)

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  8. If .^(n)C(r-1): .^(n)C(r): .^(n)C(r+1)=3:4:5, find the values of n and...

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  9. Prove that : (""^(n)C(r+1))/(""^(n)C(r))=(n-r)/(r+1)

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  10. In how many ways a committee of 7 members can be selected from 10 memb...

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  11. From a class of 30 student , 3 are to be chosen for a competition . In...

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  12. Find the number of diagonals that can be drawn by joining the angular ...

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  13. Find the number of sides of a polygon having 44 diagonals.

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  14. How many committees of 5 members each can be formed with 8 officials a...

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  15. Out of 7 consonants and 4 vowels, words are to be formed by involving ...

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  16. A box contain 5 different red and 6 different white balls. In how many...

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  17. A commttee of 8 is to be formed from 6 women and 5 men. In how many wa...

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  18. Out of the 12 professors a committee of 5 professors is to be formed ....

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  19. From a class of 12 girls and 15 boys, 12 students are to be chosen for...

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  20. In how many ways can 8 stars(**) signs and 6 triangle (Delta ) signs b...

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