Answered: From a group of 13 people how many…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

From a group of 13 people how many ways we can select a

(a) 3 Supervisor

(b) 7 Technicians

Expert Solution

Step 1

Given:

Total number of people, n=13

It is known that the formula to find different combinations is,

${}^{n}C_{r} = \frac{n!}{(n - r)! r!}$

a) To select 3 supervisors among 13 people

${}^{13}C_{3} = \frac{13!}{(13 - 3)! 3!} {}^{13}C_{3} = \frac{13!}{10! 3!} {}^{13}C_{3} = \frac{13 \times 12 \times 11 \times 10!}{10! 3 \times 2 \times 1} {}^{13}C_{3} = 13 \times 6 \times 11 {}^{13}C_{3} = 858$

Hence the number of ways in selecting 3 supervisor from 13 people is 858.

Step 2

b) To select 7 technicians among 13 people

${}^{13}C_{7} = \frac{13!}{(13 - 7)! 7!} {}^{13}C_{7} = \frac{13!}{6! 7!} {}^{13}C_{7} = \frac{13 \times 12 \times 11 \times 10 \times 9 \times 8 \times 7!}{6 \times 5 \times 4 \times 3 \times 2 \times 1 \times 7!} {}^{13}C_{7} = 13 \times 2 \times 11 \times 2 \times 3 {}^{13}C_{7} = 1716$

Hence the number of ways in selecting 3 supervisor from 13 people is 858.

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