5 A sixth-form class consists of 7 girls and 5 boys. Three students from the class are chosen at random. The number of boys chosen is denoted by the random variable \(X\). Show that
- \(\quad \mathrm { P } ( X = 0 ) = \frac { 7 } { 44 }\),
- \(\mathrm { P } ( X = 2 ) = \frac { 7 } { 22 }\).
The complete probability distribution of \(X\) is shown in the following table.
| \(x\) | 0 | 1 | 2 | 3 |
| \(\mathrm { P } ( X = x )\) | \(\frac { 7 } { 44 }\) | \(\frac { 21 } { 44 }\) | \(\frac { 7 } { 22 }\) | \(\frac { 1 } { 22 }\) |
- Calculate \(\mathrm { E } ( X )\) and \(\operatorname { Var } ( X )\).