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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. $\begin{pmatrix} 37 \\ 2 \end{pmatrix}$
asked in Combinatory by Veteran (77.2k points)   | 130 views

1 Answer

+9 votes
Best answer

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

Hence E is Answer

answered by Veteran (11.5k points)  
edited by
isn't r=3?
Yes,it was a typo...corrected it


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