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How many different ways could someone give a visitor his candy?

1-Willie Wonka gives everyone who visits his factory 9 pieces of candy to take home. He never gives a person 2 or more pieces of the same type of candy. If Mr. Wonka has 22 different types of candy, in how many different ways could Mr. Wonka give a visitor his candy?
 
2-If 165 people visit Mr. Wonka's factory each day, how many days could Mr. Wonka go without giving two visitors the same selection of candy?
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1 Answer

1-Willie Wonka gives everyone who visits his factory 9 pieces of candy to take home. He never gives a person 2 or more pieces of the same type of candy. If Mr. Wonka has 22 different types of candy, in how many different ways could Mr. Wonka give a visitor his candy?

22!/(9!(22-9)!) = 22*21*20*19*18*17*16*15*14*13!/(9!(13)!)
= 22*21*20*19*18*17*16*15*14/(9*8*7*6*5*4*3*2*1)
= 22*7*19*2*17*5
= 22*19*17*7*10
= 497,420

2-If 165 people visit Mr. Wonka's factory each day, how many days could Mr. Wonka go without giving two visitors the same selection of candy?

497420/165 = 3014.66666666666667 ≈ 3,014 days
On the 3,015th day he’s have to duplicate.