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  4. The number of solutions of the equation x+y+z = 10 in positive integers x,y,z is equal to

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Q. The number of solutions of the equation $x+y+z = 10$ in positive integers $x,y,z$ is equal to

WBJEEWBJEE 2013Binomial Theorem

Solution:

Given equation, is $x+y+z=10$
where, $x, y$ and $z$ are positive integers.
$\therefore $ Required number of solutions $={ }^{(10-1)} C_{(3-1)}$
$={ }^{9} C_{2}=\frac{9 \times 8}{2}=36$