Mr. Shah has to divide his assets worth rupees 30 crores in 3 parts to be given to three id his sons Ajay, Vijay and Arun ensuring that every son gets at least worth rupees 5 crores . In how many ways can this be done if it is given that three sons should get their shares in multiple of rupees 1 crore?.Please provide detailed solution

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Let the shares of different sons be 5+a, 5+b, and 5+c
5+a + 5+b +5+c = 30
a+b+c = 15. Now we have to find non-negative integral solutions of this equation which is given by
(n+r-1)C(r-1), so we get 17C2 = 136

Ajay+Vijay+Arun=30. Now, each of them has atleast 5 crores.
Let us assume that,
Ajay has 5+x, Vijay has 5+y and Arun has 5+z.
=> 5+x+5+y+5+z=30 =>x+y+z=15. where x,y,z are non-negative numbers. Solutions for such kind of equation is:
$$^{n+r-1}\textrm{C}_{r-1}$$, where r is the number of terms, and n is the sum of the terms.
In this case the answer will be : $$^{17}\textrm{C}_{2}$$