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Date Posted: 4 years ago
Views: 268
⁵C₃ + ⁵C₂ = ???
I think should be 5C3 x 5C2 = 100.
When 2 events are mutually exclusive (cannot both happen at same time), you add the number of ways.
Eg. If I can choose 3 different pants to wear, or 2 different shorts to wear, I can choose in total of 3+2=5 ways. They are mutually exclusive because cannot wear pants and shorts at same time.
When 2 events are not mutually exclusive, (can both happen, be it happen at same time, or happen in sequence) you multiply the number of ways.
Eg, If I can choose 3 different shirts to wear, and 2 different pants to wear, I can choose in 3x2 = 6 ways. The choice of shirt does not affect the choice of pants.
To select 3 questions from 5 for A, there are 5C3 = 10 ways.
To select 2 questions from 5 for B, there are 5C2 = 10 ways.
No matter which way you choose for A, there are still 10 ways to choose for B.
So total is 10x10 = 100 ways.
When 2 events are mutually exclusive (cannot both happen at same time), you add the number of ways.
Eg. If I can choose 3 different pants to wear, or 2 different shorts to wear, I can choose in total of 3+2=5 ways. They are mutually exclusive because cannot wear pants and shorts at same time.
When 2 events are not mutually exclusive, (can both happen, be it happen at same time, or happen in sequence) you multiply the number of ways.
Eg, If I can choose 3 different shirts to wear, and 2 different pants to wear, I can choose in 3x2 = 6 ways. The choice of shirt does not affect the choice of pants.
To select 3 questions from 5 for A, there are 5C3 = 10 ways.
To select 2 questions from 5 for B, there are 5C2 = 10 ways.
No matter which way you choose for A, there are still 10 ways to choose for B.
So total is 10x10 = 100 ways.
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