Theory question 102
Permutations and CombinationsA box contains 4 chocolate, 2 oatmeal and 14 ginger identical biscuits. If 5 biscuits are selected at random from the box, find the number of ways this can be done, if 2 must be oatmeal
Show the model answer
Model answer
Both oatmeal biscuits are chosen: ²C₂ = 1 way.
The other 3 come from the 18 non-oatmeal biscuits: ¹⁸C₃ = 816 ways.
Number of ways = 1 × 816 = 816.
Explanation
Fix the required items first, then choose the rest from what is left.