2018 EJC P2 Q11
2018 EJC P2 Q11
12 marks
Prelims
A bag contains 5 cards with the letter ‘A’, 3 cards with the letter ‘B’ and 2 cards with the letter ‘C’.
A A A A A B B B C C
The 10 cards are arranged at random in a row to form a letter sequence. For example, AABBCAAACB is a possible letter sequence.
- Find the number of possible letter sequences.[1]
- Find the number of possible letter sequences if no two ‘B’s are next to each other and no two ‘C’s are next to each other.[4]
- Find the probability that the first two letters are identical given that the second letter is not an ‘A’.[4]
The 10 cards are now arranged at random in a circle.
- Find the probability that no two ‘A’s are next to each other.[3]
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Answer:(i) \[2520\] (ii) \[966\] (iii) \[\frac{8}{45}\] (iv) \[\frac{1}{126}\]
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