Answer:
a) each flavor must be different and the order of flavors is unimportant?
31!/3!(28)!
Yes. 31C3 or (313) counts the ways to select 3 unique items from 31.
b)each flavor must be different and the order of flavors is important?
31!/(28)!
Likewise, 31P3 or (313)3! is the ways to select 3 from 31 and arrange them.
c)Flavors need not be different and the order of flavors is unimportant?(This is a non-trivial question)
33!/3!(30)!
Indeed! The "stars and bars" method counts (31+3−131−1) ways to put 3 identical items into 31 distinct boxes - or in this case take 3 scoops from 31 tubs.
Alternatively you might have counted the ways to select: three identical scoops, or a pair and a single, or three different scoops. 31+31⋅30+(313)
d) Flavors need not be different and the order of flavors is important?
31∗31∗31
Yes, 313 counts the ways to make 3 independent choices with 31 options each
Step-by-step explanation:
The customer can choose 93 options.
Important information:
We need to find the possible combinations of selecting a cone and a type of ice cream.
The number of ways of selecting a cone and a type of ice cream is:
[tex]\text{Total options}=^3C_1\times ^{31}C_1[/tex]
[tex]\text{Total options}=3\times 31[/tex]
[tex]\text{Total options}=93[/tex]
Therefore, the customer can choose 93 options.
Find out more about 'Combinations' here:
https://brainly.com/question/18095103
