Chapter 13.9, Problem 39STP

To determine

To find:The situation represented by $C\left(10,5\right)$ .

Answer to Problem 39STP

Correct option is (G) that is the number of ways to pick $5$ out of $10$ students for a project.

Explanation of Solution

Given information:

(F) The number of arrangements of $10$ people in a line.

(G) The number of ways to pick $5$ out of $10$ students for a project.

(H) The number of ways to pick $5$ out of $10$ students to be first through fifth place in a spelling bee.

(J) The number of ways $10$ people can sit in a row of $5$ chairs.

Consider (F) condition that isnumber of arrangements of $10$ people in a line.

Since the statement includes arrangement so it is example of permutation.

Consider (G) The number of ways to pick $5$ out of $10$ students for a project.

So there are $10$ students involves in a project.

As $5$ students are to be selected irrespective of any order so $5$ students can be selected as $C\left(10,5\right)$ .

Consider (H) The number of ways to pick $5$ out of $10$ students to be first through fifth place in a spelling bee.

As selection of students in spelling bee involves arrangement so it is permutation and does not represent $C\left(10,5\right)$ .

Consider (J) The number of ways $10$ people can sit in a row of $5$ chairs.

As there are $5$ chairs available and $10$ people are to be seated situation cannot be depicted clearly.

So (J) does not represent $C\left(10,5\right)$