How many ways can 12 people be divided into three groups of 2, 7 and 3 in that order?

Answer Details

In this problem, we need to find the number of ways of dividing 12 people into three groups of 2, 7 and 3 in that order. Firstly, we can choose the first group of 2 people in \(\binom{12}{2}\) ways, which gives us 66 ways. Then, we can choose the second group of 7 people from the remaining 10 people in \(\binom{10}{7}\) ways, which gives us 120 ways. Finally, the last group of 3 people is determined by the previous two groups, so there is only one way to form this group. Therefore, the total number of ways of dividing 12 people into three groups of 2, 7 and 3 in that order is the product of the number of ways of forming each group, which is equal to \(66 \times 120 \times 1 = 7,920\). Thus, the answer is 7920.