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Answer:
Step-by-step explanation:
From the given information:
A sandwich shop offers eight types of sandwiches, and Jamey likes all of them equally.
The probability that Jamey picks any one of them is 1/8
Suppose
X represents the number of times he chooses salami
Y represents the number of times he chooses falafel
Z represents the number of times he chooses veggie
Then X+Y+Z ≤ 5 and;
5-X-Y-Z represents the no. of time he chooses the remaining
8 - 3 = 5 sandwiches
However, the objective is to determine the P[X=x,Y=y,Z=z] such that 0≤x,y,z≤5
So, since he chooses x no. of salami sandwiches with probability (1/8)x
and y number of falafel with probability (1/8)y
and for z (1/8)z
Therefore, the remaining sandwiches are chosen with probability
So. these x days, y days and z days can be arranged within five days in
Thus;
since 0 ≤ x, y, z ≤ 5 and x + y + z ≤ 5.
The distribution is said to be Multinomial distribution.