Answer:
Step-by-step explanation:
Geometric sequences:
The nth term of a geometric sequence is given by the following equation.
In which r is the common ratio.
This can be expanded for the nth term in the following way:
In which is the first term.
In this question:
a. If the pattern continues, what explicit formula can be used find the distance of the nth swing?
If a department has 11 male employees and 17 female employees, then 198968 different committees of 6 members are possible with the condition that the committee has strictly more female employees than male.
As per the question statement, a department has 11 male employees and 17 female employees.
We re required to calculate the total number different committees that can be formed with 6 members strictly having more female employees than male.
Now for committee of 6 members to have more women than men, there can be two combinations:
(4 women and 2 men)
Or, (5 Women and 1 man).
That is, we will need to calculate the number of combinations we can have by selecting 4 female employees from a group of 17 and 2 Male employees from a group of 11 and the number of combinations we can have by selecting 5 female employees from a group of 17 and 1 Male employee from a group of 11 and add up the two number of combinations to obtain our required answer.
Then comes the most important thing to know to be able to solve this question, i.e., the formula to calculate combinations, which goes as
Therefore, the total number different committees that can be formed with 6 members strictly having more female employees than male is
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