Question

Eduardo, Sarah, Maria, Jim, and Tyrone 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 Eduardo arrive first and Tyrone ​last?
c. Find the probability that Eduardo will arrive first and Tyrone last.

Answer 1

Answer:

a. 120

b. 6

c. 0.05

Step-by-step explanation:

a) The ways Eduardo, Sarah, Maria, Jim, and Tyrone can arrive to the party is

5! = 5×4×3×2×1 = 120

The logic behind it is

• 5 different people can arrive first, after that

• 4 different people can arrive second, when first and second arrived is known,

• 3 different people can arrive third, then

• 2 different people can arrive fourth

• only 1 person left to be fifth.

b) Using the same logic, when first and last arrived is known, there is

3!=3×2×1=6 ways they can arrive in this case.

c)  The probability that Eduardo will arrive first and Tyrone last is

the division of the ways Eduardo arrive first and Tyrone ​last by the ways 5 people can arrive $\frac{6}{120} =0.05$