Three research departments have 6, 9, and 10 members respectively each department is to select a delegate and alternate to represent the department at a conference. in how many ways can this be done?

We have been given that three research departments have 6, 9, and 10 members respectively. Each department is to select a delegate and alternate to represent the department at a conference. We are asked to find in how many ways this can be done.

We will solve this problem using permutations because order matters in our selection.

Therefore, these selections can be done in 194400 ways.