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An English teacher gave his class a choice of $8$ books to read, $6$ of which are contemporary novels. If a student randomly picks $5$ books, what is the probability that all of them are contemporary novels? $\newline$ Write your answer as a decimal rounded to four decimal places.___

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Find probabilities using combinations and permutations

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Q. An English teacher gave his class a choice of

8

books to read,

6

of which are contemporary novels. If a student randomly picks

5

books, what is the probability that all of them are contemporary novels?

\newline

Write your answer as a decimal rounded to four decimal places.___

Total Books and Choices: Total number of books: $8$ $\newline$ Books to be chosen: $5$ $\newline$ Calculate total possible outcomes using combinations. $\newline$ Total outcomes: $_{8}C_{5}$
Calculate Total Outcomes: Find the value of $\binom{8}{5}$ . $\newline$ $\binom{8}{5} = \frac{8!}{5!(8-5)!} = \frac{8!}{5!3!} = \frac{8 \times 7 \times 6 \times 5!}{5! \times 3 \times 2 \times 1} = 56$
Calculate Total Possible Outcomes: Number of contemporary novels: $6$ Number of chosen contemporary novels: $5$ Calculate favorable outcomes using combinations. Favorable outcomes: ${}_{6}C_{5}$
Calculate Favorable Outcomes: Find the value of ${}_6C_5$ . ${}_6C_5 = \frac{6!}{5!(6-5)!} = \frac{6!}{5!1!} = \frac{6 \times 5!}{5! \times 1} = 6$
Calculate Probability: Calculate the probability that all books are contemporary novels. $\newline$ Probability = Favorable outcomes / Total possible outcomes $\newline$ = $\frac{6}{56}$ $\newline$ $\approx 0.1071$

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