Barack Obama is planning to retire soon He would like to bec

Barack Obama is planning to retire soon. He would like to become a Computer Science professor. There are 20 schools that he is interesting in. He is especially excited about the prospect of joining the University of Maryland. For your answers to these questions, you may use the combination symbol, n C m, along with the standard mathematical operations (including factorial). Do not simplify your answers.

(A) Exactly twelve of the 20 schools that Obama would like to visit are on the East Coast. How many ways can Obama visit exactly five East Coast schools and six other schools? Order matters.

(B)After playing a round of golf, Obama likes to give his hat away, so he needs many hats. Obama goes to the store to buy 30 hats. There are eight colors. How many ways can he buy hats? The order of the hats does not matter, just the number of hats of each color matters.

Solution

a)

20C5 + 20C6 = 54264

b)

30C8 = 5852925