## Related questions with answers

The Student Council at a certain school has $10$ members. Four members will form an executive committee consisting of a president, a vice president, a secretary, and a treasurer.

$\textbf{a.}\hspace{10pt}$ In how many ways can these four positions be filled?

$\textbf{b.}\hspace{10pt}$ In how many ways can four people be chosen for the executive committee if it does not matter who gets which position?

$\textbf{c.}\hspace{10pt}$ Four of the people on Student Council are Zachary, Yolanda, Xavier, and Walter. What is the probability that Zachary is president, Yolanda is vice president, Xavier is secretary, and Walter is treasurer?

$\textbf{d.}\hspace{10pt}$ What is the probability that Zachary, Yolanda, Xavier, and Walter are the four committee members?

Solution

Verified**(a)**

To determine how many ways can these four position be filled we will use the fundamental principle of counting the number of permutation.

$_nP_r=\frac{n!}{(n-r)!}$

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