alleryStart learning →Can a binomial coefficient be a fraction?
AYes, whenever r is larger than n
BNo, it is always a whole number
CYes, whenever n is an odd number
DNo, it is always a negative number
Answer & Solution
Correct answer: B. No, it is always a whole number
1. A binomial coefficient counts combinations, and a count of selections cannot be a fraction.
2. So although the formula shows a division, the factorials always divide out exactly.
3. The result is therefore always a whole number.
4. Counts are never negative either, which rules out the option claiming the value is always negative.
_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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