A dance instructor needs to select 3 men and 3 women from n married couples to form a set of 3 mixed dancing pairs. If no husband and wife can both be selected among the 6 dancers, and the total number of ways to form the set of 3 pairs is 3360 , then the value of n is

Step-by-step solution

Let the number of married couples be n . The instructor needs to select 3 men and 3 women such that no husband and wife are both selected. This means the 3 men and 3 women must come from 6 distinct couples. First, select 3 men from the n couples. This can be done in ^ n C₃ ways. Next, select 3 women from the remaining n-3 couples (to ensure no spouses of the selected men are chosen). This can be done in ^ n-3 C₃ ways. Now, we have 3 men and 3 women. The number of ways to pair them into a set of 3 mixed dancing pair