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If .^(2n)C(3):^(n)C(3)=11:1, find the va...

If `.^(2n)C_(3):^(n)C_(3)=11:1`, find the value of n.

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We have, ltBrgt `.^(2n)C_(3):^(n)C_(3)=11:1`
`implies(.^(2n)C_(3))/(.^(n)C_(3))=(11)/(1)`
`implies((2n(2n-1)(2n-2))/(1*2*3))/((n(n-1)(n-2))/(1*2*3))=11implies(4(2n-1))/((n-2))=11`
`implies8n-4=11n-22implies3n=18`
`thereforen=6`
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ARIHANT MATHS-PERMUTATIONS AND COMBINATIONS -Exercise (Questions Asked In Previous 13 Years Exam)
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  6. The letters of the word COCHIN are permuted and all the permutation...

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  8. Consider all possible permutations of the letters of the word ENDEANOE...

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  9. The number of words can be formed with the letters of the word 'MATHEM...

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  10. In a shop, there are five types of ice-creams available. A child buys ...

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  13. There are two urns. Urn A has 3 distinct red balls and urn B has 9 ...

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  14. In how many ways 5 different balls can be distributed into 3 boxes so ...

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  15. There are 10 points in a plane, out of these 6 are collinear. The numb...

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  16. The total number of ways in which 5 balls of differert colours can be ...

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  17. Let n denote the number of all n-digit positive integers formed by the...

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  18. Let a(n) denote the number of all n-digit numbers formed by the digits...

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  19. Assuming the balls to be identical except for difference in colours, t...

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  20. Let Tn be the number of all possible triangles formed by joining ve...

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