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Name: 12 sales representatives for company are to be chosen at random to par
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Description: 12 sales representatives for company are to be chosen at random to participate in a training program the company has 18 sales rep representatives three in each of the six regions what is the probability that the 12 sales representatives chosen to par

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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12 sales representatives for company are to be chosen at random to participate in a training program the company has 18 sales rep representatives three in each of the six regions what is the probability that the 12 sales representatives chosen to participate in the training program will be from only four of the six regions

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Given Information:

12 sales representatives for company are to be chosen at random to participate in a training program.

The company has 18 sales rep representatives three in each of the six regions.

To find the probability that the 12 sales representatives chosen to participate in the training program will be from only four of the six regions:

Probability of an event is given by the formula:

$P (E) = \frac{f a v o u r a b l e o u t c o m e s}{T o t a l p o s s i b l e o u t c o m e s}$

Number of ways of selecting 12 sales representatives from a total of 18 is done in ${}^{18}C_{12}$ ways.

That is: ${}^{18}C_{12} = \frac{18!}{12! (18 - 12)!} = \frac{18 \times 17 \times 16 \times 15 \times 14 \times 13 \times 12 \times 11 \times 10 \times 9 \times 8 \times 7 \times 6!}{12 \times 11 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 \times 6!} = 18564$

Since, there are three sales representatives per region, the 12 selected sales representatives are from only 4 of the 6 regions.

So, number of ways of selecting 4 regions from a total of 6 is done in ${}^{6}C_{4}$ ways. That is:

$\begin{array}{rcl} {}^{6}C_{4} & = & \frac{6!}{4! (6 - 4)!} \\ = & \frac{6 \times 5 \times 4 \times 3 \times 2!}{4 \times 3 \times 2 \times 1 \times 2!} \\ = & \frac{360}{24} \\ = & 15 \end{array}$

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