Question

tyrone, kim, sarah, eduardo, and simone 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 tyrone arrive first and simone last?
c. find the probability that tyrone will arrive first and simone last.
a. 120 (type an integer.)
b. 6 (type an integer.)
c. \\(\square\\) (type a fraction. simplify your answer.)

Explanation:

Step1: Recall Probability Formula

Probability of an event is the number of favorable outcomes divided by the total number of possible outcomes. Here, favorable outcomes (Tyrone first, Simone last) are 6 (from part b), total outcomes are 120 (from part a).

Step2: Calculate Probability

Probability = $\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$ = $\frac{6}{120}$

Step3: Simplify the Fraction

Simplify $\frac{6}{120}$ by dividing numerator and denominator by 6: $\frac{6\div6}{120\div6}$ = $\frac{1}{20}$

Answer:

$\frac{1}{20}$