7 Sharma knows that she has 3 tins of carrots, 2 tins of peas and 2 tins of sweetcorn in her cupboard. All the tins are the same shape and size, but the labels have all been removed, so Sharma does not know what each tin contains. Sharma wants carrots for her meal, and she starts opening the tins one at a time, chosen randomly, until she opens a tin of carrots. The random variable \(X\) is the number of tins that she needs to open.

1. Show that \(\mathrm { P } ( X = 3 ) = \frac { 6 } { 35 }\).
2. Draw up the probability distribution table for \(X\).
3. Find \(\operatorname { Var } ( X )\).
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