alleryStart learning →How is the binomial coefficient written as n over r calculated?
AAs n! / (r!(n - r)!)
BAs n! / (r!(n + r)!)
CAs n! / ((n - r)!)
DAs r! / (n!(n - r)!)
Answer & Solution
Correct answer: A. As n! / (r!(n - r)!)
1. The coefficients in a binomial expansion are combinations, since each term counts how many ways a choice can be made.
2. So the binomial coefficient written as n over r is the same number as C(n, r).
3. That value is n! divided by r!(n - r)!.
4. Dividing only by (n - r)! gives P(n, r), the permutation count, which is larger because it keeps order in play.
_Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 13 "Sequences, Probability and Counting Theory", section 13.6 Binomial Theorem_
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