Twelve cards, numbered from $1$ to $12$ are arranged in a straight line. Find the number of ways

Question

Twelve cards, numbered from $1$ to $12$ are arranged in a straight line. Find the number of ways this can be done if there are no restrictions,[1] the cards numbered $2$ and $3$ are together, and all the six even numbered cards are adjacent.[3] The twelve cards are arranged in a circle. Find the number of ways this can be done if all the cards numbered as multiples of $3$ are separated.[2] Six of the cards are selected at random, without replacement. Find the probability that at least two of the chosen cards are even numbered.[3]

Accepted Answer

(i) $479001600$ (ii) $172800$ (iii) $8467200$ (iv) $\frac{887}{924}$(or $0.960$)

2018 VJC P2 Q5

2018 VJC P2 Q5

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