Question

Katrina, Maria, Sergio, Larry, and lan 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 Katrina arrive first and lan last? c. Find the probability that Katrina will arrive first and lan last.

Answer 1

Part A

In how many ways can they arrive?

Find out the permutation P5

`\begin{gathered} P5=5!=5*4*3*2*1 \\ P5=120 \end{gathered}`

The answer Part a is 120 ways

Part B

In how many ways can Katrina arrive first and lan last?

1) Katrina

2) Maria, Sergio, Larry (3)

3) Maria, Sergio, Larry (2)

4) Maria, Sergio, Larry (1)

5) Ian

the number of ways is=(1)(3)(2)(1)(1)=6

The answer Part B is 6 ways

Part C

Find the probability that Katrina will arrive first and lan last.

P=6/120

simplify

P=1/20