You are Here: Home >< Maths

# Numbers and Counting question watch

1. I am confused by the following question, the second part of (a) and (b). For (a) I got 560, which I know is correct. When it talks about removing the hats, I got the answer 28, when the solutions say it's 280.

14. (a) 8 people are to be divided into three teams, distinguished by the colour hats they wear.
2 people will wear red hats, 3 green hats and 3 blue hats. How many ways are there of
choosing the teams? What if we remove the hats so that the two teams of size three become
interchangeable?
(b) 8 people are to be divided into four teams, distinguished by hat colour: 2 people will wear
red hats, 2 green hats, 2 blue hats and 2 orange hats. How many ways are there of choosing
the teams? What if we remove the hats?

Anyone help?
2. (Original post by theereflex)
I am confused by the following question, the second part of (a) and (b). For (a) I got 560, which I know is correct. When it talks about removing the hats, I got the answer 28, when the solutions say it's 280.

14. (a) 8 people are to be divided into three teams, distinguished by the colour hats they wear.
2 people will wear red hats, 3 green hats and 3 blue hats. How many ways are there of
choosing the teams? What if we remove the hats so that the two teams of size three become
interchangeable?
(b) 8 people are to be divided into four teams, distinguished by hat colour: 2 people will wear
red hats, 2 green hats, 2 blue hats and 2 orange hats. How many ways are there of choosing
the teams? What if we remove the hats?
The second part of 14(a) means the following scenarios are now the same since there are no hats:

Green hats: A, B, C
Blue hats: X, Y, Z

Green hats: X, Y, Z
Blue hats: A, B, C

Hence there should be half the number of possibilities in the first part of 14(a).

### 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: January 14, 2017
Today on TSR

### He broke up with me because of long distance

Now I'm moving to his city

### University open days

Wed, 25 Jul '18
2. University of Buckingham
Wed, 25 Jul '18
3. Bournemouth University
Wed, 1 Aug '18
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
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}