CW #48 - Fundamental Counting Principle

Front

What is the Fundamental Counting Principle?

Back

The Fundamental Counting Principle states that if one event can occur in 'm' ways and a second event can occur independently in 'n' ways, then the total number of ways both events can occur is m x n.

Front

How many different license plates can be formed with 3 letters followed by 3 numbers without repetition?

Back

26 x 25 x 24 x 10 x 9 x 8 = 11,232,000

Front

If Marissa has 8 T-shirts and 6 pairs of shorts, how many different outfits can she create?

Back

8 x 6 = 48

Front

What is the total number of outcomes when rolling two number cubes, spinning a spinner with 4 colors twice, and flipping two coins?

Back

2,304

Front

How many four-letter passwords can be formed using the letters A, B, C, and D if repetition is allowed?

Back

4 x 4 x 4 x 4 = 256

Front

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

Back

5 x 8 x 2 = 80

Front

What is the formula for calculating the number of combinations of 'n' items taken 'r' at a time?

Back

C(n, r) = n! / (r!(n - r)!)

Front

What is the difference between permutations and combinations?

Back

Permutations consider the order of selection, while combinations do not.

Front

How do you calculate the total number of outcomes for independent events?

Back

Multiply the number of outcomes for each event.

Front

What is the significance of the factorial symbol 'n!' in counting problems?

Back

The factorial 'n!' represents the product of all positive integers up to 'n' and is used in permutations and combinations.