Question

Vishnu is headed to a the world golf championship, which has a total of  90 players. 17 players are from the United States, 36 are French, and 37 are Canadian. To gauge the talent of the event Vishnu invites ten players randomly chosen for a practice round.

a. What is the probability that the practice group contains exactly 1 player from the united states, 5 Frenchmen, and 4 Canadians?

b. What is the probability that 1 of the players selected to participate in the practice round is from the United States?

c. What is the probability that Vishnu sits with the best player at dinner after the practice round if the table is round and seating is random? (assume Vishnu is not the best player)

Answer 1

Total number of ways to select 10 players from 90 players is

a) the total number of ways to select 1 player from the united states, 5 Frenchmen, and 4 Canadians is

the probability that the practice group contains exactly 1 player from the united states, 5 Frenchmen, and 4 Canadians =

b) The probability that 1 of the players selected to participate in the practice round is from the United States =

c) The number of ways 11 people including Vishnu can be seated round the table = 10! = 3628800

This is also the number of ways that 11 people can be seated at a round table if we choose a particular point to be the beginning and end of the row. But there are 11 possible such points. So there are 11 ways of seating 11 people abreast for every way of seating them at a round table. It follows that the number of ways of seating 11 people at a round table = 11!/11 = 10! = 362,8800.

Total number of ways vishnu can sit with the best is

Here suppose that vishnu and the best player is clubbed and they can e arrange in 2 ways within themselves, now we are left with 10 people that can be arrange in 9! ways round the table. hence 2*9!

The required probability =