Permutations, Combinations, FCP

Front

What is a permutation?

Back

A permutation is an arrangement of objects in a specific order. The order matters in permutations.

Front

What is a combination?

Back

A combination is a selection of objects where the order does not matter.

Front

What is the Fundamental Counting Principle (FCP)?

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 two events can occur in m × n ways.

Front

How many ways can 5 dogs (3 black, 2 tan) be arranged in a Black-Tan-Black-Tan-Black pattern?

Back

The arrangement is a permutation problem. The answer is 3! (for black) × 2! (for tan) = 12 ways.

Front

If a lock has 3 dials with 10 digits each and repetition is allowed, how many possible codes can be formed?

Back

Using FCP, the total number of codes is 10 × 10 × 10 = 1000.

Front

How many different license plates can be made with 3 letters followed by 4 digits, allowing repetition?

Back

Using FCP, the total is 26^3 (for letters) × 10^4 (for digits) = 17,576,000.

Front

What is empirical probability?

Back

Empirical probability is the probability based on observed data, representing what actually happens.

Front

When selecting a President and Vice President from 10 candidates, is it a permutation or combination?

Back

It is a permutation because the order of selection matters.

Front

What is the formula for permutations of 'n' objects taken 'r' at a time?

Back

The formula is P(n, r) = n! / (n - r)!.

Front

What is the formula for combinations of 'n' objects taken 'r' at a time?

Back

The formula is C(n, r) = n! / [r!(n - r)!].