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:

Step-by-step solution

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 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