Distinct ways are there to split 50 identical coins among three people so that each person gets at least 5 coins
x_{1}+5+x_{2}+5+x_{3}+5 = 50
x_{1}+x_{2}+x_{3} = 35
Solving Non integral solution n=35 ,r =3
^{n+r-1 }C _{r-1 }= ^{35+3-1} C _{3-1 }= ^{37} C_{ 2}
Hence E is Answer