Canada's Wonderland has the following attractions, all rated as"Agressive thrill rides":

• Nine roller coasters
• Seven carnival rides
• Five water slides

Pat always rides roller coasters first (which are fun), thencarnival rides (which make Pat sick), then water slides (which Patfinds refreshing). Order matters to Pat so, for example, if herides The Behemoth and then the DragonFyre, that's different than riding the DragonFyre and then the Behemoth.

1. If Pat wants to ride one attraction of each type (rollercoaster, water slide, carnival ride), then how many options does hehave?
2. If Pat wants to ride two attractions of each type and doesn'tmind riding the same attraction twice, then how many options doeshe have?
3. If Pat wants to ride two attractions of each type and doesn'twant to ride the same attraction twice, then how many options doeshe have?
4. If Pat wants to ride rollercoasters 20 times and doesn't wantto ride the same rollercoaster twice in a row, then how manyoptions does he have?