Problema Solution
There are 7 erasers to collect from free cereal boxes. All the children want want to collect the whole set. they all have different collections and none have more than one of any eraser. What is the maximum number of children there could be at the school?
Answer provided by our tutors
Since none of any of the children have the same collections. The number of options must equal the maximum number of children. First, we will find the number of combinations for children having 1 eraser in their collection up to 7 erasers. Then we will add these combinations to get the maximum number of children:
General equation: n!/[r!(n-r)!] where n is the number of things to choose from (7 in this case) and r is the number of them that you are choosing.
1 eraser : 7!/[1!(7-1)!] = 7!/6! = 7
2 erasers: 7!/[2!(7-2)!] = 7!/(2!5!) = 21
3 erasers: 7!/[3!(7-3)!] = 7!/(3!4!) = 35
4 erasers: 7!/[4!(7-4)!] = 7!/(4!3!) = 35
5 erasers: 7!/[5!(7-5)!] = 7!/(5!2!) = 21
6 erasers: 7!/[6!(7-6)!] = 7!/(6!1!) = 7
7 erasers: 7!/[7!(7-7)!] = 7!/(7!0!) = 1
Total number of combinations:
7+21+35+35+21+7+1=127