You are Here: Home >< Maths

# Combinations Help watch

1. A box of 20 biscuits contains 4 different chocolate biscuits, 2 different oatmeal biscuits and 14 different ginger biscuits. 6 biscuits are selected from the box at random.
(i) Find the number of different selections that include the 2 oatmeal biscuits.

So I've tried using :
Excluding oatmeal = 18C2, No restrictions = 20C6
Selections = 20C6 - 18C2
=20196

But the correct answer is 18C4 = 3060

I understand the answer's method, but could someone explain why my initial method is incorrect? Thanks
2. (Original post by sourmango1)
A box of 20 biscuits contains 4 different chocolate biscuits, 2 different oatmeal biscuits and 14 different ginger biscuits. 6 biscuits are selected from the box at random.
(i) Find the number of different selections that include the 2 oatmeal biscuits.

So I've tried using :
Excluding oatmeal = 18C2, No restrictions = 20C6
Selections = 20C6 - 18C2
=20196

But the correct answer is 18C4 = 3060

I understand the answer's method, but could someone explain why my initial method is incorrect? Thanks
For your approach to work, you would have to calculate it as unrestricted combinations - combinations with neither of the oatmeals - combinations with exactly one of the oatmeals. This would leave you with the combinations with two oatmeals as required. You have omitted the third element.

(Also I'm guessing you mean 18C6 where you've written 18C2).
3. (Original post by old_engineer)
For your approach to work, you would have to calculate it as unrestricted combinations - combinations with neither of the oatmeals - combinations with exactly one of the oatmeals. This would leave you with the combinations with two oatmeals as required. You have omitted the third element.

(Also I'm guessing you mean 18C6 where you've written 18C2).
Ah yes I meant 18C6. Thank you I understand now.

### Related university courses

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: October 13, 2017
Today on TSR

### Exam Jam 2018

Join thousands of students this half term

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams