Solve the problem.
-A software company employs 9 sales representatives and 8 technical representatives.How many ways can the company select 5 of these employees to send to a computer convention if at least 4 technical representatives must attend the convention?
A)1440
B)180
C)686
D)360

Question

Quizplus · Accepted Answer

We can use combinations to solve this problem.
First, we choose 4 technical representatives out of 8:
${8 \choose 4} = 70$
Then, we choose 1 additional representative from the remaining 17 (9 sales reps and 8 technical reps):
${17 \choose 1} = 17$
The total number of ways to choose 5 representatives with at least 4 technical reps is:
$70 * 17 = 1190$
However, we must also take into account that all 5 representatives can be technical representatives, which gives us an additional:
${8 \choose 5} = 56$ ways
Therefore, the total number of ways to select 5 representatives is:
$1190 + 56 = 1246$
So the answer is not one of the given choices. But the closest one is C, which is off by only 4 (1246-686=560), suggesting a possible typographical error in the options.

Solve the Problem. -A Software Company Employs 9 Sales Representatives and 8 Technical