Question:
If $a$ and $b$ denote respectively the coefficients of $x^{m}$ and $x^{n}$ in the expansion of $(1+x)^{m+n}$, then write the relation between $a$ and $b$.
Solution:
Coefficient of $x^{m}$ in the given expansion $={ }^{m+n} C_{m}=a$
Coefficient of $x^{n}$ in the given expansion $={ }^{m+n} C_{n}=b$
$\therefore a=b \quad\left[\because{ }^{m+n} C_{m}={ }^{m+n} C_{n}\right]$
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