2018 YJC P2 Q7
Ten cards each has a single letter or a digit written on them. The letters are A, B, C, D, E and the digits are $1$, $2$, $3$, $4$, $5$.
(i)
Find the number of ways in which the $10$ cards can be divided into two sets with each set consisting of $5$ cards.
[1]
Find the number of ways of arranging the ten cards in a row such that
(ii)
all the consonants are next to each other and all the digits are next to each other,
[2]
(iii)
the letters must be in alphabetical order from left to right.
[2]
The ten cards are now arranged at random in a circle.
(iv)
Find the probability that no two odd digits are next to each other.
[3]
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