Answer :
Answer:
16.67% probability that Jeremy will select an outfit that includes flip-flops (F) and argyle (A) socks
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes. To find the number of outcomes, we use the permutations formula.
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
Desired outcomes:
One shirt, from a set of 2.
One pant, from a set of 2.
Argyle socks.
Flip flops.
So
[tex]D = P_{{2,1)}*P_{{2,1)} = 4[/tex]
Total outcomes:
One shirt, from a set of 2.
One pant, from a set of 2.
One sock, from a set of 2.
One footwear, from a set of 3.
So
[tex]T = P_{{2,1)}*P_{{2,1)}*P_{{2,1)}*P_{{3,1)} = 24[/tex]
Probability:
[tex]p = \frac{D}{T} = \frac{4}{24} = 0.1667[/tex]
16.67% probability that Jeremy will select an outfit that includes flip-flops (F) and argyle (A) socks