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 \(1\), \(2\), \(3\), \(4\), \(5\).

1. 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

2. all the consonants are next to each other and all the digits are next to each other,[2]
3. the letters must be in alphabetical order from left to right.[2]

The ten cards are now arranged at random in a circle.

4. Find the probability that no two odd digits are next to each other.[3]