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How many distinct ways are there to split 50 identical coins among three people so that each person gets at least 5 coins?

1. $3^{35}$
2. $3^{50}-2^{50}$
3. $\begin{pmatrix} 35 \\ 2 \end{pmatrix}$
4. $\begin{pmatrix} 50 \\ 15 \end{pmatrix}. 3^{35}$
5. $\begin{pmatrix} 37 \\ 2 \end{pmatrix}$

Distinct ways are there to split 50 identical coins among three people so that each person gets at least 5 coins

x1+5+x2+5+x3+5 = 50

x1+x2+x3 = 35

Solving Non integral solution n=35 ,r =3

n+r-1 C r-1 = 35+3-1 C 3-1 = 37 C 2

edited
isn't r=3?
Yes,it was a typo...corrected it