Question:
What is the number of distinct terms in the expansion of \((a + b + c)^{20}\)?
What is the number of distinct terms in the expansion of \((a + b + c)^{20}\)?
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The number of terms in a multinomial expansion equals the number of non-negative integer solutions to the exponent sum equation.
Updated On: Jul 30, 2025
- 231
- 242
- 243
- 210
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The Correct Option is A
Solution and Explanation
Number of distinct terms in \((a+b+c)^{n}\) = number of non-negative integer solutions to:
\[
x + y + z = n
\]
where \(x, y, z\) are exponents of \(a, b, c\).
Formula: \(\binom{n+3-1}{3-1} = \binom{n+2}{2}\).
For \(n = 20\):
\[
\binom{22}{2} = 231
\]
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