Complete Question
Of a company's personnel, 7 work in design, 14 in manufacturing, 4 in testing, 5 in sales, 2 in accounting and 3 in marketing. A committee of 6 people is to be formed to meet with upper management.Lucy works in the design department and her husband Ricky works in marketing. In how many ways can the committee be formed if they cannot both be on the committee together
Answer:
The value is [tex]F = 1582240 \ ways[/tex]
Step-by-step explanation:
Generally the total number of personnel in the company is mathematically evaluated as
[tex]N = 7 + 14 + 4 + 5 + 2 + 3[/tex]
=> [tex]N =35[/tex]
The number of personnel that are to make up the committee is n = 6
Generally the number of ways of selecting the 6 person committee from the total number of personnel in the company is mathematically represented as
[tex]n = ^{35}C_{6}[/tex]
=> [tex]n = 1.62316 * 1 0^6[/tex]
Here C stands for combination hence we are going to be making use of the combination function in our calculators
Generally the number of ways of selecting 6 person committee from the total number of personnel without including Lucy and the husband Ricky is
[tex]k = ^{35 - 2} C_{6-2}[/tex]
=> [tex]k = ^{33} C_{4}[/tex]
=> [tex]k = 40920[/tex]
Generally the number of way of selecting the committee in such a way that Lucy and the husband are not on the committee together is mathematically evaluated as
[tex]F = 1.62316 * 1 0^6 - 40920[/tex]
=> [tex]F = 1582240 \ ways[/tex]
