11) Calculate: the following Combinations and Permutation a) c? b) P10 c) P?
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
![### Combinations and Permutations Problems
#### Problem 11: Calculate the following Combinations and Permutations:
**a)** \(\binom{9}{6}\)
**b)** \( _{8}P_{10} \)
**c)** \( _{5}P_{7} \)
These problems involve calculating combinations and permutations, which are fundamental concepts in combinatorics used to count or arrange objects.
**Explanation:**
1. **Combinations (\(\binom{n}{r}\)) :**
The number of ways to choose \(r\) objects from \(n\) without regard to the order of selection.
The formula for combinations is given by:
\[
\binom{n}{r} = \frac{n!}{r!(n-r)!}
\]
2. **Permutations (\(P(n, r)\)) :**
The number of ways to arrange \(r\) objects from \(n\) distinct objects where the order does matter.
The formula for permutations is:
\[
P(n, r) = \frac{n!}{(n-r)!}
\]
If there are graphical elements such as diagrams or detailed calculations, they can be illustrated alongside these explanations to enhance understanding.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F56b8dc5f-7385-41ed-8a38-17c82f9077b4%2F46676162-63e0-453b-a97a-076f44c437f2%2Fnrkdhzm.png&w=3840&q=75)
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