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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
![[(17C4)*(11C2)+(17C5)*(11C1)]\\=[(2380*55)+(6188*11)]\\=(130900+68068)\\=198968](https://tex.z-dn.net/?f=%5B%2817C4%29%2A%2811C2%29%2B%2817C5%29%2A%2811C1%29%5D%5C%5C%3D%5B%282380%2A55%29%2B%286188%2A11%29%5D%5C%5C%3D%28130900%2B68068%29%5C%5C%3D198968)
- combination(s): In mathematics, a combination is a way of selecting items from a collection or set, where the order of selection does not matter, i.e., for example, we have a set of three numbers X, Y and Z and then, in how many ways can we select two numbers from each set, is defined by combination.
To learn more about Combinations, click on the link below.brainly.com/question/8044761
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Answer:
Step-by-step explanation:
The volume of the rectangular prism is 1120 yd³.
<h3>What is a prism?</h3>
A prism is a solid geometric figure whose two ends are similar, equal, and parallel rectilinear figures, and whose sides are parallelograms.
To calculate the volume of the rectangular prism, we use the formula below.
Formula:
- V = LWH.......... Equation 1
Where:
- V = Volume of the rectangular prism
- L = Length of the prism
- W = Width of the prism
- H = Height of the prism.
From the question,
Given:
- L = 14 yards
- W = 8 yards
- H = 10 yards.
Substitute thee values into equation 1
Hence, The volume of the rectangular prism is 1120 yd³.
Learn more about prism here: brainly.com/question/12691050
Answer:
121π
Step-by-step explanation:
The formula for a circle is πr^2. But if given a diameter instead of radius, you simply divide by 2 because radius is half of a diameter.
Radius of this circle is 11 because you divide 22 by 2.
Then you follow the formula. 11^2=121.