Abeka Algebra 2 Quiz 35

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

Factorial is represented by an exclamation point.

The notation for combination is C.

What is the value of 5!?

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

What is the value of P?

What is the value of C?

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

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

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

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.

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.