a) Find the number of different ways that the 9 letters of the word $HAPPINESS$ can be arranged in a line.
b) The 9 letters of the word $HAPPINESS$ are arranged in random order in a line. Find the probability that the 3 vowels $\left( {A,{\text{ }}E,{\text{ }}I} \right)$ are not all next to each other.
c) Find the number of different selections of 4 letters from the 9 letters of the word $HAPPINESS$ which contain no $P\,s$ and either one or two $S\,s$.
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