A marching band consists of 11 pipers and 12 drummers. Three of them are selected to march in order in a scaled-down socially-distanced New Year parade. How many different possibilities are there if the selected trio must include at least one drummer?

Since you want to select at least one drummer from a group of 12 and two pipers from a group of 11, the total number of possibilities would be the sum of combinations for selecting 1 drummer and 2 pipers, 2 drummers and 1 piper, and 3 drummers: Combinations (nCr) = n! / (r! * (n - r)!) So, the total possibilities = C(12, 1) * C(11, 2) + C(12, 2) * C(11, 1) + C(12, 3) C(12, 1) = 12 C(11, 2) = 55 C(12, 2) = 66 C(11, 1) = 11 C(12, 3) = 220 Now, sum up the combinations: 12 * 55 + 66 * 11 + 220 = 660 + 726 + 220 = 1606 So, there are 1606 different possibilities if the selected trio must include at least one drummer.