Question 1030400: if thirteen baskets are arranged and three fruits of different types are put in each basket,,,,, in each basket a fruit is picked randomly, find the possible solutions of the thirteen picks [fruit1-mango,fruit2-orange,fruit3-lemon].......if for instance the first solution is [1,1,1,1,1,1,1,1,1,1,1,1,1]
Answer by mathmate(429)   (Show Source):
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Question:
if thirteen baskets are arranged and three fruits of different types are put in each basket,,,,, in each basket a fruit is picked randomly, find the possible solutions of the thirteen picks [fruit1-mango,fruit2-orange,fruit3-lemon].......if for instance the first solution is [1,1,1,1,1,1,1,1,1,1,1,1,1]
Solution:
This is a permutation with repetitions permitted.
The number of choices at each basket is 3.
For the next basket, the number of choices is still three (repetitions permitted), so there are 3*3=9 choices for two baskets.
For the third basket, the number of choices is still three, so there is a total of 3*3*3=3³ choices.
Continue this until the thirteenth basket, we will have 313=1594323 choices, which is a little long to enumerate here.
However, the first and last ones would look like:
1111111111111
1111111111112
1111111111113
1111111111121
1111111111122
1111111111123
1111111111131
...
...
3333333333331
3333333333332
3333333333333
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