Permutations vs Combinations in Binomial Models
A student uses a binomial model to compute the probability that exactly 3 out of 8 lightbulbs are defective. By treating the outcomes as ordered events, the student overcounts the number of possible arrangements. Which of the following best describes this error?
A
Assuming that defective probabilities are additive rather than multiplicative.
B
Incorrectly using permutations instead of combinations, thereby overcounting the number of defective arrangements.
C
Using the wrong exponent on the defective probability when applying the binomial formula.
D
Confusing the binomial distribution with the Poisson distribution and applying the wrong formula.
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