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junior college 2 | H2 Maths
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Mark Tan
Mark Tan

junior college 2 chevron_right H2 Maths chevron_right Singapore

Q3 please help.
Thanks

Date Posted: 4 years ago
Views: 254
J
J
4 years ago
Complement way :

Total cases : 13C8 = 1287

Case 1 : Only 1 of the 3 tallest players inside the team

3C1 (pick 1 of the 3)
x 10C7 (pick 7 of the 10 remaining players)

= 360

Case 2 : None of the 3 tallest players inside the team

10C8 (pick 8 of the remaining 10 players)
= 45

Case 3 : Both shortest players inside, 2 of 3 tallest players inside

3C2 (pick 2 of the 3 tallest)
x 2C2 (pick both shortest players, you can skip writing this since it's just 1 way)
x 8C4 (pick 4 from the remaining 8)

= 210

Case 4 : Both shortest players inside, all 3 tallest players inside

3C3 (pick all 3 tallest players, you can skip writing this since it's just 1 way)
x 2C2 (pick both shortest players, you can also skip writing this since it's just 1 way)
x 8C3 (pick 3 players from the remaining 8)

= 56


Required cases = total - these cases

= 1287 - 360 - 45 - 210 - 56
= 616

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lim
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