therronvictorjr
27.06.2020 •
Mathematics
A company sells regular hamburgers as well as a larger burger. Either type can include cheese, relish, lettuce, tomato, mustard, or ketchup. a. How many different hamburgers can be ordered with exactly 4 extras? b. How many different regular hamburgers can be made that use any 4 of the extras? c. How many different regular hamburgers can be ordered with at least 3 extras?
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Ответ:
a. 30
b. 15
c. 42
Step-by-step explanation:
We have two types of hamburgers and six types of extras.
a.
To find the number of different burgers with 4 extras, we have a combination of 6 choose 4 to find the number of possibilities for the extras, and we have that amount of possibilities for each of the two types of burger, so we have:
2 * C(6,4) = 2 * 6! / (4! * 2!) = 2 * 6 * 5 / 2 = 30 different hamburgers.
b.
The number of different regular hamburgers is half the number of different burgers found above:
C(6,4) = 6! / (4! * 2!) = 6 * 5 / 2 = 15 different hamburgers.
c.
We want at least 3 extras, so we can have 3, 4, 5 or 6 extras, then we need to calculate combinations of 6 choose 3, 4, 5 and 6:
3 extras: C(6,3) = 6! / (3! * 3!) = 6 * 5 * 4 / 3 * 2 = 20 different hamburgers.
4 extras: C(6,4) = 6! / (4! * 2!) = 6 * 5 / 2 = 15 different hamburgers.
5 extras: C(6,5) = 6! / (5! * 1!) = 6 / 1 = 6 different hamburgers.
6 extras: C(6,6) = 6! / (6! * 0!) = 1 different hamburger.
Total: 20 + 15 + 6 + 1 = 42 different regular burgers
Ответ:
=0
Step-by-step explanation: