Product principle, permutations and combinations.
Example 1
A club has 8 students. How many different committees of 2 students can be chosen?
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Answer: 28
- A committee is unordered, so use combinations.
- Choose 2 from 8:nCr=28.
Example 2
From 9 runners, how many ordered first, second and third places are possible, with no ties?
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Answer: 504
- There are 9 choices for first, then 8 for second, then 7 for third.
- Multiply: 504.
Example 3
A code has one of 5 letters followed by 5 digits. Each digit can be 0–9 and repeats are allowed. How many codes are possible?
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Answer: 500000
- There are 5 choices for the letter and 10 for each digit.
- By the product principle: 5×105=500000.