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Find `""^(18)C_(3)+^(18)C_(2)`

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To solve the problem \( ^{18}C_{3} + ^{18}C_{2} \), we can use the identity for combinations: ### Step 1: Use the Combination Identity We know from the combination identity that: \[ ^{n}C_{r} + ^{n}C_{r-1} = ^{n+1}C_{r} \] In our case, \( n = 18 \) and \( r = 3 \). Thus, we can rewrite the expression as: ...
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If ^(18)C_(x)=^(18)C_(x+2),f in dx

(i) If .^(20)C_(r)=.^(20)C_(r+6) , find r. (ii) If .^(18)C_(r)=.^(18)C_(r+2) , find .^(r)C_(5) .

The coefficient of x^(8)y^(10) in the expansion of (x+y)^(18) is ^(18)C_(8) b.^(18)P_(10) c.2^(18) d.none of these

If ""^(18)C_(15)+2(""^(18)C_(16))+""^(17)C_(16)+1=""^(n)C_(3) , then n is equal to :

Set of values of r for which, .^(18)C_(r-2)+2.^(18)C_(r-1)+ ^(18)C_(r) ge .^(20)C_(13) contains

If ^(^^)18C_(r)=^(18)C_(r+2) then prove that ^^^rC_(5)=56.

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AAKASH INSTITUTE-PERMUTATIONS AND COMBINATIONS -Try Yourself
  1. If ""^(n)C(10)=""^(n)C(13) , then find the value of ""^(n)C(2)

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

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

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

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

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

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

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

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

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  11. How many committee of 5 members each can be formed with 8 officials an...

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

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

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

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

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

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

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  18. In how many ways can 10 identical shirts and 7 identical trousers be p...

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  19. In how many ways 4 different white balls and 6 different black balls b...

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  20. In how many ways can 7 boys and 2 girls be seated in a row so that two...

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