Answered: From a group of 13 people how many…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter9: Sequences, Probability And Counting Theory

Section: Chapter Questions

Problem 32RE: In a group of 20 musicians, 12 play piano, 7 play trumpet, and 2 play both piano and trumpet. How...

See similar textbooks

Related questions

Concept explainers

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.

Step by step

Solved in 3 steps

Knowledge Booster

$Fundamental Counting Principle$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.

Similar questions