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100 POINTS!! NEED ANSWER WITH WORK ASAP!!
Coach Bennet’s high school basketball team has 14 players, consisting of six juniors and eight seniors. Coach Bennet must select three players from the team to participate in a summer basketball clinic.
How many different groups of three players are possible for Coach Bennet to select?

100 POINTS NEED ANSWER WITH WORK ASAP Coach Bennets High School Basketball Team Has 14 Players Consisting Of Six Juniors And Eight Seniors Coach Bennet Must Sel class=

Answer :

Answer:

See below ~

Step-by-step explanation:

This is a combination because the order in which the players are selected is not important.

Number of ways

  • 14! / 11! 3!
  • 14 x 13 x 12 x 11! / 11! x 3 x 2
  • 14 x 13 x 2
  • 364 ways

Apply combination

[tex]\\ \rm\Rrightarrow ^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]

So

[tex]\\ \rm\Rrightarrow ^{14}C_3[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{14!}{3!(14-3)!}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{14(13)(12)(11!)}{3!11!}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{14(13)(12)(11)}{6}[/tex]

[tex]\\ \rm\Rrightarrow 14(13)(2)(11)[/tex]

[tex]\\ \rm\Rrightarrow 4004[/tex]

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