Abeka Algebra 2 Quiz 35

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.