Jim, Katrina, Larry, and Jim 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 Jim arrive first and Kim ​last?
c. Find the probability that Jim will arrive first and Kim last.

a.___ (Type an integer)
b.___ (Type an integer.)
c.___ (Type a fraction. Simplify your answer)

24

6

1/12

Step-by-step explanation:

a) This is a counting problem 4*3*2*1 = 24 different ways.

b) 1 * 2 * 1 * 1   = 2 ways

This is one you should try.

Jim Kat Larry Kim

Jim Larry Kat Kim

You can't get another way.

c)

There are 2 ways that Jim can arrive first and Kim Last shown in b

2/24 = 1/12

i) 4!=24

ii) 2 ways

iii) 2/24=1/12

Answered by gauthmath.

step-by-step explanation:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

step-by-step explanation:

given that megan owns a clothing boutique.

the profits of 2010, 11, are recorded and shown as follows:

years since     2010 0     1     2     3       4       5

profits made in 1000's   39       84     111     120   111     84

we find that profit gradually increases form 2010 to 2013 upto 120,   then starts decreasing.

the profits for 2012 and 2014 are the same while that of 2011 and 2015 are also the same.

this shows that there is symmetry about the line profit = 120000

hence answer is:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

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