Question 1189891: Determine the sample space illustrated in each situation below.
A farmer has three fields, each of which must be planted with rice or corn. He does not plant the same crop in all three fields. Generating a tree diagram, list all the elements of the sample space (S)
Answer by ikleyn(52890)   (Show Source):
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Determine the sample space illustrated in each situation below.
A farmer has three fields, each of which must be planted with rice or corn.
He does not plant the same crop in all three fields.
Generating a tree diagram, list all the elements of the sample space (S)
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By coding the fields with letters R (rice) and C (corn),
the set of all 8 possible outcomes is the set of all words of the length 3
written in 2-letter alphabet {R,C}.
In all, there are  = 8 such words
1 2 3 4 5 6 7 8
RRR, RRC, RCR, RCC, CRR, CRC, CCR, CCC.
From these 8 words, we EXCLUDE two of them, RRR and CCC, due to imposed restriction
(he does not plant the same crop in all three fields).
So, the sample space can be represented by the remaining 6 words
2 3 4 5 6 7
RRC, RCR, RCC, CRR, CRC, CCR.
Solved.
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