Question

(1 point) Rework problem 4 from section 2.2 of your text, involving the choice of officers for acommittee. For this problem, assume that you have a committee of 10 members, and that youmust choose a parliamentarian, and secretary.msIn how many ways can these selections be made?

Answer 1

There are 90 possible ways the selection can be made

Here, we want to know the number of ways the choice can be made from 10 members

Firstly, we want to select 1 parliamentarian from 10 members; then after the selection we will select a secretary from the remaining nine

As pertaining selections, selecting r items from a total n , can be calculated by the use of the combinatorial formula as follows;

$\begin{gathered} ^nC_r\text{ = }\frac{n!}{(n-r)!r!_{}} \\ \\ \text{Also, we have;} \\ ^nC_1\text{ = n} \end{gathered}$

So, we have 10 ways to select an item from 10 items, we also have 9 ways to select an item from 9 items

So, the total possible number of ways would be;

$10\times\text{ 9 = 90 ways}$