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junior college 1 | H1 Maths
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Date Posted: 3 years ago
Views: 376
M - Male
F - Female
It can be either 4M & 1F, 3M & 2F, or 2M & 1F.
7C4 x 6C1 = 210
7C3 x 6C2 = 525
7C2 x 6C3 = 420
210+525+420= 1155 ways
Pls check :)
F - Female
It can be either 4M & 1F, 3M & 2F, or 2M & 1F.
7C4 x 6C1 = 210
7C3 x 6C2 = 525
7C2 x 6C3 = 420
210+525+420= 1155 ways
Pls check :)
Complement method :
If there isn't at least 2 male and 1 female mice, the possible scenarios are :
① 1 male mouse only, 4 female
② all female mice
③ all male mice
Number of ways for :
① 7C1 × 6C4 = 7 x 15 = 105
② 6C5 = 6
③ 7C5 = 21
Total number of ways for ①,②,③
= 105 + 6 + 21
= 132
Total number of days if there is no restriction
= 13C5
= 1287
Number of ways for the required cases
= 1287 - 132
= 1155
If there isn't at least 2 male and 1 female mice, the possible scenarios are :
① 1 male mouse only, 4 female
② all female mice
③ all male mice
Number of ways for :
① 7C1 × 6C4 = 7 x 15 = 105
② 6C5 = 6
③ 7C5 = 21
Total number of ways for ①,②,③
= 105 + 6 + 21
= 132
Total number of days if there is no restriction
= 13C5
= 1287
Number of ways for the required cases
= 1287 - 132
= 1155
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