MCQ

The coefficient of *x*^{8} *y*^{10} in the expansion of (*x* + *y*)^{18} is

#### Options

^{18}*C*_{8}^{18}*p*_{10}2

^{18}none of these

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#### Solution

^{18}*C*_{8}

\[\text{ Suppose the (r + 1)th term in the given expansion contains } x^8 y^{10} . \]

\[\text{ Then, we have } \]

\[ T_{r + 1} =^{18}{}{C}_r x^{18 - r} y^r \]

\[\text{ For the coefficient of } x^8 y^{10} \text{ We have} \]

\[r = 10\]

\[\text{ Hence, the required coefficient is }^{18}{}{C}_{10} \text{ or } ^{18}{}{C}_8\]

Concept: Introduction of Binomial Theorem

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