Question

simone, dawn, katrina, maria, sarah, ian, eduardo, and kim have all been invited to a dinner party. they arrive randomly and each person arrives at a different time.

a. in how many ways can they arrive?
b. in how many ways can simone arrive first and kim last?
c. find the probability that simone will arrive first and kim last.

a. (type an integer)

Explanation:

Count the total number of people

We count the total number of individuals invited to the dinner party: Simone, Dawn, Katrina, Maria, Sarah, Ian, Eduardo, and Kim.

$$ n = 8 $$

Calculate total arrival arrangements

Using the Permutations knowledge point

$$ 8! = 40,320 $$

Calculate restricted arrival arrangements

Using the Permutations knowledge point

$$ 1 \times 6! \times 1 = 720 $$

Calculate the probability

Using the Probability knowledge point

$$ P = \frac{720}{40,320} = \frac{1}{56} $$

Answer:

Question a

In how many ways can they arrive? <blank>40320</blank>

Question b

In how many ways can Simone arrive first and Kim last? <blank>720</blank>

Question c

Find the probability that Simone will arrive first and Kim last. <blank>\(\frac{1}{56}\)</blank>