3
QuizMultiple Choice

The Binomial Theorem

Question 3 • Adv. Algebra II S1 Original

Which statement about the simplified binomial expansion of (a + b)n, where n is a positive integer, is true?

Answer
A
The value of the binomial coefficient nC0 is n – 1 for all values of n.
B
The values of nC1 and nCn–1 are equal to 1.
C
The values of nC0 and nCn are equal to 1.
D
The value of the binomial coefficient nC1 is n – 1 for all values of n.

Explanation

For a positive integer n, choosing 0 items from n items can be done in exactly 1 way, so nC0 = 1. Choosing all n items can also be done in exactly 1 way, so nCn = 1. Therefore, the true statement is that nC0 and nCn are both equal to 1.

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