Question

Question 1

Answer 1

Using the permutation and the combination formula, we have that:

a) The first three finishers can be awarded medals in 504 ways.

b) They can be arranged in 252 ways.

c) In how many ways can 4 students form a team from a set of 8.

• If the order is important, the permutation formula is used.

• If the order is not important, the combination formula is used.

Combination formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by:

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

Permutation formula:

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

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

Item a:

Order is important, as the finishers are ranked, hence:

$P_{(9,3)} = \frac{9!}{6!} = 504$

The first three finishers can be awarded medals in 504 ways.

Item b:

The order is not important, hence:

$C_{10,5} = \frac{10!}{5!5!} = 252$

They can be arranged in 252 ways.

Item c:

Situation in which the order is not important, hence, for example, in how many ways can 4 students form a team from a set of 8.

For more on permutation/combination, you can take a look at brainly.com/question/25247153