A automobile race contains 15 racecars. In how many ways can the racecars finish in first, second, and third place?

A committee is to be formed with a president, vice-president, and a secretary. There are 10 people to be selected from. How many committees are possible?

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 piper?

2. Molly really enjoyed country music. After listening one afternoon to her favorite station foran hour, she had heard 25 songs. All but 1 song were about either truck drivers, being in love,hound-dog owners, or some combination of the three. She noted the following information: Allof the truck drivers were in love. Three-fourths of the truck drivers were not hound-dogowners. There were six hound-dog owners who were in love. Of the hound-dog owners whowere not truck drivers, half of them were in love. Eighty percent of all the songs concernedpeople in love. How many songs concerned people who were in love but were neither truckdrivers nor hound-dog owners?