A committee of three people is selected at random from a set consisting of six teachers, three parents of students, and seven alumni.a. What is the probability of the event that the committee consists of all teachers?b. What is the probability of the event that the committee has no teachers?a. The probability the committee consists of all teachers is.(Type an integer or a simplified fraction.)b. The probability the committee has no teachers is.(Type an integer or a simplified fraction.)Enter your answer in each of the answer boxes.Prt Scn.HomeDII* 12F3F1

Answered: A committee of three people is selected…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A committee of three people is selected at random from a set consisting of six teachers, three parents of students, and seven alumni.
a. What is the probability of the event that the committee consists of all teachers?
b. What is the probability of the event that the committee has no teachers?
a. The probability the committee consists of all teachers is.
(Type an integer or a simplified fraction.)
b. The probability the committee has no teachers is.
(Type an integer or a simplified fraction.)
Enter your answer in each of the answer boxes.
Prt Scn.
Home
DII
* 12
F3
F1

Expert Solution

Step 1

Given, Total number of teachers= 6

Number of parents = 3

Number of Alumni = 7

Committee of 3 is to be chosen,

$\begin{array}{rcl} P (c o m m i t e e c o n s i s t o f a l l t e a c h e r s) & = & \frac{N u m b e r o f p o s s i b l e w a y s}{T o t a l n u m b e r o f w a y s} \\ = & \frac{{}^{6}C_{3}}{{}^{16}C_{3}} = \frac{\frac{6!}{3! 3!}}{\frac{16!}{13! 3!}} \\ P (c o m m i t e e c o n s i s t o f a l l t e a c h e r s) & = & \frac{6 \times 5 \times 4}{16 \times 15 \times 14} = \frac{120}{3360} = \frac{1}{28} \end{array}$

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