InterviewSolution
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InterviewSolution
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Given that `C(n, r) : C(n,r + 1) = 1 : 2 and C(n,r + 1) : C(n,r + 2) = 2 : 3`. What is r equal to ?A. 2B. 3C. 4D. 5 |
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Answer» Correct Answer - C `(.^(n)C_(r))/(.^(n)C_(r+1))=(1)/(2)` `(|ul(n)|ul(r+1)|ul(n-r-1))/(|ul(r)|ul(n-r).|ul(n))=(1)/(2)` `(r+1)/(n-r)=(1)/(2)rArr 3r -n+2=0" "...(i)` `(.^(n)C_(r+1))/(.^(n)C_(r+2))=(2)/(3)` `(|ul(n)|ul(r+2)|ul(n-r-2))/(|ul(r+1)|ul(n-r-1)|ul(n))=(2)/(3)` `(r+2)/(n-r-1)=(2)/(3)rArr 5r - 2n + 8 = 0` Solving equation (i) and (ii), we get `n = 14, r = 4` |
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