Find the number of integral solution of the equation $$x + y + z = 20$$ and $$x > - 1, y > - 2$$ and $$z > - 3.$$
A.
$$^{25}{C_{23}}$$
B.
$$^{17}{C_{2}}$$
C.
$$^{23}{C_{2}}$$
D.
None of these
Answer :
$$^{25}{C_{23}}$$
Solution :
Since as per the give condition $$x > - 1,$$ so $$x$$ is non negative integer, $$y > - 2$$ so $$y = - 1 + b$$ and similarly $$z > 3$$ so $$z = - 2 + c$$
or, $$\left( x \right) + \left( { - 1 + b} \right) + \left( { - 2 + c} \right) = 23$$
or, $$x + b + c = 23$$
and we need to find the number of non negative integral solution of the equation $$x + b + c = 23$$ which is,
$$^{23 + 3 - 1}{C_{3 - 1}} = {\,^{25}}{C_2} = {\,^{25}}{C_{23}}$$
Releted MCQ Question on Algebra >> Permutation and Combination
Releted Question 1
$$^n{C_{r - 1}} = 36,{\,^n}{C_r} = 84$$ and $$^n{C_{r + 1}} = 126,$$ then $$r$$ is:
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