1.Sammy the samurai has 18 different sais. 7 are newly sharpened, and the rest are long overdue for a sharpening. Unfortunately, his roommate William did not know the difference and dumped them all into a sack. Sammy needs a sai to cut the green onions for his udon soup so he will plunge his hand in the sack and draw out 8 sais. If at least 3 are newly sharpened, he will cut his finger off. what is the probability he gets to keep his fingers?

2.sammy has finished eating his udon and wants to cleanse his palate with some tea. He goes down to the tea house and sees his fellow samurai friends playing a fun game where they throw down three stiletto daggers at once. Each stiletto is red on one side and blue on the other. Because samurais are incredibly skilled at throwing knives, each dagger has an equal chance of landing with blue facing up, red facing up, or on its edge. It costs $50 to play but if you throw exactly one stiletto on red, one on blue, and one on edge, then you win $60 and if you throw each stiletto facing the same way then you win $30; otherwise you win nothing. Should Sammy play the game?

3.Sammy is training for an upcoming battle. He is practice fighting is friend. He has a 78% chance of winning each time they duel. The practice fight is best of 7, what is the probability that Sammy will win the fight.

4.In Sammy's clan, there are 60 members, 12 of which are ninjas and the rest samurai. If 6 teams are formed from random selection, what is the probability that a team will have less than 3 ninjas.