Respuesta :
The theoretical probability that applesauce and broccoli will both offered on monday is 20%.
What is combination?
A combination is a way of selecting items from a collection where the order of selection does not matter. It is calculated by
[tex]^{n} C_{r} = \frac{n!}{(n-r)!}[/tex]
Where,
[tex]^{n} C_{r}[/tex] is the total number of combinations.
n is the total number of objects
r is the number of objects selected.
What is theoretical probability?
The theoretical probability is defined as the ratio of the number of favourable outcomes to the number of possible outcomes.
According to the question.
There are total 6 dishes.
Manger have to choose three dishes for monday.
Now the total number of combination of selecting 3 dishes from 6 dishes
[tex]=^{6} C_{3}[/tex]
[tex]= \frac{6!}{3!(6-3)!}[/tex]
[tex]= \frac{6\times5\times4\times3!}{3\times2\times1\times3!}[/tex]
[tex]=20[/tex]
So, the manager has total 20 choices to select three dishes randomly out or 6 dishes.
Also, it is given that for monday applesauce and broccolli will both offered so the number of choices or combination or the three dishes will be
- Applesauce, broccoli, and corn
- applesauce, brocolli, and dumplings
- applesauce, brocolli, and egg rolls
- applesauce, brocolli, and french fries
Therefore, the theoretical probability that applesauce and brocoli will both be offered on monday
[tex]= \frac{4}{20}\times100[/tex]
[tex]= \frac{1}{5} \times 100\\= 20\%[/tex]
Hence, the theoretical probability that applesauce and broccoli will both offered on monday is 20%.
Find out more information about combination and theoretical probability here:
https://brainly.com/question/1064256
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