7. A bag contains \(n\) marbles of which 7 are green.
From the bag, 3 marbles are selected at random.
The random variable \(X\) represents the number of green marbles selected.
The cumulative distribution function of \(X\) is given by
| \(x\) | 0 | 1 | 2 | 3 |
| \(\mathrm {~F} ( x )\) | \(a\) | \(b\) | \(\frac { 37 } { 38 }\) | 1 |
- Show that \(n ( n - 1 ) ( n - 2 ) = 7980\)
- Verify that \(n = 21\) satisfies the equation in part (a).
Given that \(n = 21\)
- find the exact value of \(a\) and the exact value of \(b\)
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