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Tucker is filling out summer job applications, so that he can earn money to buy a car. Of the $9$ jobs he's applying for, $7$ are tutoring jobs. $\newline$ If Tucker randomly picks $6$ applications to submit today, what is the probability that all of them are for tutoring jobs? $\newline$ Write your answer as a decimal rounded to four decimal places. $\newline$ ____ $\newline$

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Find probabilities using combinations and permutations

Full solution

Q. Tucker is filling out summer job applications, so that he can earn money to buy a car. Of the

9

jobs he's applying for,

7

are tutoring jobs.

\newline

If Tucker randomly picks

6

applications to submit today, what is the probability that all of them are for tutoring jobs?

\newline

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

\newline

____

\newline

Calculate Total Outcomes: Total number of job applications: $9$ \ Number of applications to submit: $6$ \ Calculate the total number of ways to choose $6$ out of $9$ applications.\ Total outcomes: $\binom{9}{6}$
Find Value of $9C6$ : Find the value of $_9C_6$ .
$_9C_6 = \frac{9!}{6!(9-6)!} = \frac{9 \times 8 \times 7 \times 6!}{6! \times 3 \times 2 \times 1} = 84$
Calculate Favorable Outcomes: Number of tutoring job applications: $7$ $\newline$ Number of tutoring applications to submit: $6$ $\newline$ Calculate the number of ways to choose $6$ out of $7$ tutoring applications. $\newline$ Favorable outcomes: $\binom{7}{6}$
Find Value of $7C6$ : Find the value of $_7C_6$ .
$_7C_6 = \frac{7!}{6!(7-6)!} = \frac{7 \times 6!}{6! \times 1} = 7$
Calculate Probability: Calculate the probability that all $6$ applications submitted are for tutoring jobs. $\newline$ Probability $= \frac{\text{Favorable outcomes}}{\text{Total possible outcomes}}$ $\newline$ $= \frac{7}{84}$ $\newline$ $= 0.0833$ when rounded to four decimal places.

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