Question

a commercial for glade plug-ins says that by inserting 2 of a choice of 11 scents into the device, you can make more than 50 combinations. if we exclude the boring choice of two of the same scent, how many possibilities are there?

Answer 1

If we exclude the choice of two of the same scent, we can choose two different scents out of 11 in 11 choose 2 ways, which is:

11 choose 2 = (11!)/(2!*(11-2)!) = 55

Therefore, there are 55 possible combinations of two scents using 11 available scents in which two of the same scent is excluded.