4 The random variable \(X\) is equally likely to take any of the \(n\) integer values from \(m + 1\) to \(m + n\) inclusive. It is given that \(\mathrm { E } ( 3 X ) = 30\) and \(\operatorname { Var } ( 3 X ) = 36\). Determine the value of \(m\) and the value of \(n\). 526 cards are each labelled with a different letter of the alphabet, A to Z. The letters A, E, I, O and U are vowels.

1. Five cards are selected at random without replacement. Determine the probability that the letters on at least three of the cards are vowels.
2. All 26 cards are arranged in a line, in random order.
   1. Show that the probability that all the vowels are next to one another is \(\frac { 1 } { 2990 }\).
   2. Determine the probability that three of the vowels are next to each other, and the other two vowels are next to each other, but the five vowels are not all next to each other.