Answer:
a) 720, b) 475020, c) 69300, d) 0.146, e) 0.001
Step-by-step explanation:
It is given that my friend has 10 bottles of zinfandel, 8 of merlot, and 11 of cabernet.
a)
If he wants to serve 3 bottles of zinfandel and serving order is important, then the total number of ways is
Therefore if he wants to serve 3 bottles of zinfandel and serving order is important, then the total number of ways are 720.
b)
The total number of bottles is
Combination is defined as
where, n is total possible outcomes and r is selected outcomes.
we have to select 6 bottles out of 29. so,
Therefore ff 6 bottles of wine are to be randomly selected from the 29 for serving, then the total number of ways are 475020.
c)
If we want to select 2 bottles of each variety, then total number of ways are
Therefore if 6 bottles are randomly selected with two bottles of each variety, then the total possible ways are 69300.
d)
Probability is defined as
Therefore the probability that two bottles of each variety being chosen is 0.146.
e)
If 6 bottles are randomly selected, then the probability that all of them are the same variety is
Therefore if 6 bottles are randomly selected, then the probability that all of them are the same variety is 0.001.