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shreya visits the cities A, B, C and D at random. What is the probability that he visits 1) A before B 2) A just before B

shreya visits the cities A, B, C and D at random. What is the probability that he visits
1) A before B 2) A just before B

Grade:Upto college level

1 Answers

Latika Leekha
askIITians Faculty 165 Points
9 years ago
Shreya visits 4 cities A, B, C and D. the various possible orders in which he visits these cities can be
ABCD, ABDC, ACBD, ACDB, ADBC, ADCB.
Similarly, if he visits the city B first, then the possibilities are
BACD, BADC, BCAD, BCDA, BDAC, BDCA.
Now, similarly for C and D,
CABD, CADB, CBAD, CBDA, CDBA, CDAB.
DABC, DACB, DBAC, DBCA, DCAB, DCBA.
Hence, in total there are 24 outcomes.
Now, we consider the following parts:
(i) A before B
There are exactly 12 cases in which A is before B.
Hence, the required probability = 12/24 = ½
(ii) A just before B
Count the number of cases in which A and B are together and A is just before B
Probability = 5/24.
Thanks & regards Latika Leekha
askIITians Faculty

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