Question

Six students are running for the positions of president and vice-president, and five students are running for secretary and treasurer. If the two highest vote getters in each of the two contests are elected, how many winning combinations can there be?

Answer 1

Using the permutation formula, it is found that there can be 600 winning combinations.

There are roles involved(president, vice-president, secretary and treasures), hence the order is important and the permutation formula is used.

What is the permutation formula?

The number of possible permutations of x elements from a set of n elements is given by:

$P_{(n,x)} = \frac{n!}{(n-x)!}$

In this problem:

• For president and vice-president, 2 students are chosen from a set of 6.

• For secretary and treasurer, 2 students are chosen from a set of 5.

Hence:

$T = P_{6,2}P_{5,2} = \frac{6!}{4!} \times \frac{5!}{3!} = 30 \times 20 = 600$

There can be 600 winning combinations.

More can be learned about the permutation formula at brainly.com/question/25925367