fundamental counting principle flashcard

Front

What is the Fundamental Counting Principle?

Back

The Fundamental Counting Principle states that if there are 'm' ways to do one thing and 'n' ways to do another, then there are m × n ways to do both.

Front

How do you calculate the total number of outfit combinations?

Back

Multiply the number of options for each clothing item. For example, if there are 3 shirts, 2 pants, and 2 shoes, the total combinations are 3 × 2 × 2 = 12.

Front

What does a tree diagram represent in counting problems?

Back

A tree diagram visually represents all possible outcomes of a sequence of events, helping to organize and count combinations.

Front

If a student council has 24 members, how many ways can you select a president, vice-president, treasurer, historian, and secretary?

Back

The number of ways to select these positions is calculated using permutations: 24 × 23 × 22 × 21 × 20 = 5,100,480.

Front

How many outfits can be made with 5 pairs of jeans, 8 t-shirts, and 2 pairs of shoes?

Back

Total outfits = 5 × 8 × 2 = 80.

Front

What is the probability of an event not occurring, denoted as P(not A)?

Back

P(not A) = 1 - P(A). If P(A) = 1/4, then P(not A) = 3/4.

Front

What is a combination in counting?

Back

A combination is a selection of items where the order does not matter. For example, choosing 2 fruits from a basket of 5.

Front

What is a permutation in counting?

Back

A permutation is an arrangement of items where the order matters. For example, arranging 3 books on a shelf.

Front

How do you find the total number of combinations of outfits with different clothing items?

Back

Use the formula: Total combinations = (number of shirts) × (number of pants) × (number of shoes).

Front

What is the significance of simplifying probabilities?

Back

Simplifying probabilities makes them easier to understand and compare. For example, 6/8 simplifies to 3/4.