A catering service offers 6 ​appetizers, 9 main​ courses, and 5 desserts. A banquet committee is to select 3 ​appetizers, 6 main​ courses, and 3 desserts. How many ways can this be​ done?

A rock group needs to choose 3 songs to play at the annual Battle of the Bands. How many ways can they choose their set if have 15 songs to pick from?

Susan bought 20 plants to arrange along the border of her garden. How many distinct arrangements can she make if the plants are comprised of 6 tulips, 6 roses, and 8 daisies?

An art store has 4 brands of paint pens in 12 different colors and 3 types of ink. How many paint pens are there to choose from?

Hector wants to place billboard advertisements throughout the county for his new business. How many ways can Hector choose 15 neighborhoods to advertise in if there are 30 neighborhoods in the county?

A self-serve frozen yogurt shop has 8 candy toppings and 4 fruit toppings to choose from. How many ways are there to top a frozen yogurt?

In a competition of 50 professional ballroom dancers, 22 compete in the fox-trot competition, 18 compete in the tango competition. and 6compete in both the fox-trot and tango competitions. How many dancers compete in the foxtrot or tango competitions?