Let 0 ≤ r ≤ n . If ^ n+1 C_ r+1 : ^n C_ r : ^ n-1 C_ r-1 =55: 35: 21 , then 2 n+5 r is equal to:

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Correct answer: A. 50

aligned & ^ n+1 C_r ^n C_r =(55)/(35) & ((n+1) !)/((r+1) !(n-r)) ! (r !(n-r) !)/(n !)=(11)/(7) & ((n+1))/(r+1)=(11)/(7) aligned aligned & 7 n=4+11 r & ^n C_r ^ n-1 C_ r-1 =(35)/(21) & (n !)/(r !(n-r) !)=((r-1) !(n-r) !)/((n-1) !)=(5)/(3) & (n)/(r)=(5)/(3) & 3 n=5 r & By solving r=6 n=10 & 2 n+5 r=50 aligned

Let 0 ≤ r ≤ n . If ^ n+1 C_ r+1 : ^n C_ r : ^ n-1 C_ r-1 =55: 35:...

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