Question

In how many ways could eight students be placed into two groups of any size,as long as there are at least two in a group?Explain your reasoning.

Answer 1

Let say there are 2 person in group 1 and 6 person in group 2.

so total number of ways = 8C2 * 6C6 = 28

there are 3 person in group 1 and 5 person in group 2.

so total number of ways = 8C3 * 5C5 = 56

there are 4 person in group 1 and 4 person in group 2.

so total number of ways = 8C4 * 4C4 = 70

there are 5 person in group 1 and 3 person in group 2.

so total number of ways = 8C5 * 3C3 = 56

there are 6 person in group 1 and 2 person in group 2.

so total number of ways = 8C6 * 2C2 = 28

so total number of ways = 28 + 56 + 70 + 56 + 28 = 238