Question

1-87a. while waiting for a bus after school, renae programmed her mp3 player to randomly play two songs from her playlist, below. assume that the mp3 player will not play the same song twice.

playlist
a. i love my mama
(country)
by the strings of heaven
b. don’t call me mama
(country) duet
by sapphire and hank
tumbleweed
c. carefree and blue (r &
b)
by sapphire and prism
escape
d. go back to mama
(rock) duet
by bjorn free and
sapphire
e. smashing lollipops
(rock)
by sapphire

a sample space is a list of all possible outcomes for a
probabilistic situation. list the sample space for all the
combinations of two songs that renae could select. the
order that she hears the songs does not matter for your
list.

how can you be sure that you listed all of the song
combinations?

you should find 10 different possible combinations. you
will need this information for the next few problems.
make sure you can find all 10 combinations on your
own.

○ i found all ten combinations! i am confident i
can do it again in the future.

○ 10? i have no idea how there are 10
combinations!

Explanation:

Step1: Identify the songs

The songs are labeled a, b, c, d, e.

Step2: List combinations (order doesn't matter)

Start with a: (a,b), (a,c), (a,d), (a,e)
Then b (excluding a): (b,c), (b,d), (b,e)
Then c (excluding a,b): (c,d), (c,e)
Then d (excluding a,b,c): (d,e)
Count: \(4 + 3 + 2 + 1 = 10\) combinations.

Answer:

The sample space (all 2 - song combinations) is:
(a, b), (a, c), (a, d), (a, e),
(b, c), (b, d), (b, e),
(c, d), (c, e),
(d, e)

To ensure all are listed, use the combination formula \(C(n,k)=\frac{n!}{k!(n - k)!}\) where \(n = 5\) (songs) and \(k = 2\) (songs per combination). \(C(5,2)=\frac{5!}{2!3!}=\frac{5\times4}{2\times1}=10\), and the step - by - step pairing (starting with each song and pairing with subsequent ones) also gives 10, confirming completeness.