# A local high school soccer team has 20 players. (See images) Need solving this, it’s all one problem! Facts to consider for solving this problem:

A local high school soccer team has 20 players. (See images) Need solving this, it’s all one problem! Facts to consider for solving this problem: For part 1, We’re asking how many ways the 1st 2nd and 3rd horses could be.  Let H = {h_0, h_1, … h_11} be the 12 horses in the race.  Here are two example ways the “podium” can be arranged: (h_3, h_7, h_2), (h_9, h_0, h_11) For part 3, It refers to a specific one of the 6 defenders that the team has in part ii. So, yes we assume the name of this singular player is “Jack”. Assume the player does not have to play. Transcribed Image Text: Simplify each binomial coefficient or permutations to factorial fractions:
п!
n!
P(n, k) =
=
k
(n – k)!k!
(п — К)!
You need not simplify these expressions, such as 154 or 17!, in your response. Transcribed Image Text: i. In how many ways can the coach choose 11 players to play?
ii. A lineup describes the set of players which play together. A lineup consists of:
4 midfielders, 3 defenders, 3 attackers and 1 goalkeeper.
This team has:
7 midfielders, 6 defenders, 5 attackers and 2 goalkeepers
in total on their roster. In how many ways can the coach choose a lineup of players?
iii. Now assume that one of the defenders, after a summer or practice, may play the attack position
in addition to defense. In how many ways can the coach choose a lineup?