Question

find the probability of guessing the top five winners (in any order) from a group of 16 finalists in a spelling bee.

the probability that someone correctly predicts the top five winners from a group of 16 finalists is .
(type an integer or a fraction.)

Explanation:

Calculate total possible outcomes

Using the Combinations knowledge point

$$ \binom{16}{5} = \frac{16 \times 15 \times 14 \times 13 \times 12}{5 \times 4 \times 3 \times 2 \times 1} = 4368 $$

Calculate the probability

Using the Probability knowledge point

$$ P = \frac{1}{4368} $$

Answer:

The probability that someone correctly predicts the top five winners from a group of 16 finalists is <blank>\(\frac{1}{4368}\)</blank>.