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?

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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A local high school soccer team has 20 players. (See images)

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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: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.
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?
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?
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