A biscuit tin contains 4 chocolate, 2 oatmeal, and 14 ginger biscuits. If 5 biscuits are selected at random, how many selections contain exactly 2 oatmeal biscuits?

There are 4 chocolate, 2 oatmeal, and 14 ginger biscuits.
Total biscuits = $4 + 2 + 14 = 20$.
We need to select 5 biscuits, and 2 of them must be oatmeal.

Since there are 2 oatmeal biscuits available and we must select 2, the number of ways to do this is given by the combination formula $C(n, k) = \frac{n!}{k!(n-k)!}$:

There is only 1 way to select 2 oatmeal biscuits from the 2 available.

We need to select a total of 5 biscuits. Since 2 oatmeal biscuits have already been selected, we need to select $5 - 2 = 3$ more biscuits.
These remaining 3 biscuits must come from the chocolate and ginger biscuits, as the oatmeal biscuits have been fully accounted for.
The number of chocolate and ginger biscuits available is $4 + 14 = 18$.
The number of ways to select 3 biscuits from these 18 is:

To find the total number of ways to select the 5 biscuits with the given condition, multiply the number of ways from Step 2 and Step 3:

The number of ways this can be done is 816.