## Questions and Answers

A ______________ is the number of ways to select individuals out of a group in any order.

combination

Factorial is represented by an exclamation point.

True

The notation for combination is C.

True

What is the value of 5!?

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What is the value of 3!(4-1)!?

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What is the value of P?

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What is the value of C?

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How many possible combinations are there for a 3-digit security code using the numbers 0-9 if the numbers can be repeated?

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How many ways can 3 officers be elected from a senior class of 36 students?

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If a bag contains 18 different colored marbles, how many different samples of 3 marbles can be drawn from the bag?

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## Study Notes

### Combinations and Factorials

- A combination refers to the number of ways to select individuals from a group without concern for the order of selection.
- Factorial notation is represented by an exclamation point (e.g., n!).
- The notation for combinations is denoted as "C".

### Factorial Calculations

- The value of 5! (5 factorial) is calculated as 5 × 4 × 3 × 2 × 1, which equals 120.
- The expression 3!(4-1)! translates into 3! × 3!, yielding a result of 36.

### Permutations and Combinations

- The value represented by P is 6720, indicating a permutation calculation involving specific arrangements.
- The value represented by C is 1140, indicating a combination calculation for selecting a group.

### Combinatorial Applications

- A 3-digit security code formed using numbers 0-9 allows for 1000 possible combinations when numbers can be repeated.
- For the election of 3 distinct officers (president, vice president, secretary) from a senior class of 36 members, there are 42,840 different ways to select candidates.

### Sample Selection

- Drawing samples from a group, such as selecting 3 marbles from 18 differently colored marbles, results in 816 unique combinations.

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## Description

Test your knowledge on combinations and factorials with this set of flashcards from Abeka Algebra 2 Quiz 35. Each card features a key concept or definition to reinforce your understanding of combinatorial mathematics and permutations.