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If ""^(15)C(x)=""^(15)C(x+3) , then fi...

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

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To solve the equation \( \binom{15}{x} = \binom{15}{x+3} \), we can use the property of combinations that states if \( \binom{n}{r} = \binom{n}{s} \), then \( r + s = n \). ### Step-by-step Solution: 1. **Identify the values**: We have \( n = 15 \), \( r = x \), and \( s = x + 3 \). 2. **Set up the equation**: ...
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AAKASH INSTITUTE ENGLISH-PERMUTATIONS AND COMBINATIONS -Try Yourself
  1. Find n if ""^(n)C(4)=""^(n)C(6)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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