A woman has 10 close friends whom she wants to invite to her birthday dinner.

Question

a. In how many ways can she invite 8 or more friends to her party?

b. In how many ways can she seat her 10 friends around a circular table?

Answer 1

You need the PICK formula

(N pick k) = N! / (N-k)!

# of ways to arrange all 10 of them:

(10 pick 10) = 10!/(10-10)! = 10!/0! = 10!/1 = 10!

# of ways to arrange 9 of them

(10 pick 9) = 10! / (10-9)! = 10! / 1! = 10!

# of ways to arrange 8 of them:

(10 pick 8) = 10! / (10-8)! = 10! / 2! = 10*9*8*7*6*5*4*3