Teacher+Page

===This page is for teachers who want to use the BBI Maths Trail as a learning tool in their classroom maths. For each of the fifteen questions on the BBI Maths Trail, there is an explanation of the question, the solution, the method and recommended teaching methods for that question.===

**Question 15**
This problem is requires advanced probability functions like permutations (in form of //n//!/(//n-r//)!) //n// being the amount of things (in this case People) and //r// Being the ways they can be placed.

For example: In this problem //n// is 12 and //r// is be 3,4,5,6,7,8,9,10,11 or 12. So in the first example //n// is 12 and //r// is 3. Therefore: 12!/(12-3)! =   12!/9!=    12P3 (12 permute 3) = 1320.   Since the problem goes all the way up to 12 we keep adding the permutations together.

12P3+ 12P4+ 12P5+ 12P6 + 12P7 +12P8+ 12P9+ 12P10+ 12P11+ 12P12= 1,302,061,200 possible ways.