AlgII 11.1 Permutations & Combinations -G2

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. It focuses on the group rather than the arrangement.

Front

How do you calculate the number of permutations of n objects?

Back

The number of permutations of n objects is calculated as n! (n factorial), which is the product of all positive integers up to n.

Front

How do you calculate the number of combinations of n objects taken r at a time?

Back

The number of combinations is calculated using the formula: C(n, r) = n! / (r! * (n - r)!), where n is the total number of objects and r is the number of objects to choose.

Front

What is the factorial of a number?

Back

The factorial of a number n, denoted as n!, is the product of all positive integers from 1 to n.

Front

Calculate 5! (5 factorial).

Back

5! = 5 × 4 × 3 × 2 × 1 = 120.

Front

If there are 10 players, how many ways can they be arranged in a line?

Back

The number of arrangements is 10! = 3,628,800.

Front

How many ways can a president, vice-president, and secretary be elected from 125 juniors?

Back

The number of ways is P(125, 3) = 125! / (125 - 3)! = 1,906,500.

Front

How many ways can Lily choose 3 pies from 8 available pies?

Back

The number of ways is C(8, 3) = 8! / (3! * (8 - 3)!) = 56.

Front

What is the formula for calculating arrangements of letters in a word with repeated letters?

Back

The formula is: n! / (n1! * n2! * ... * nk!), where n is the total letters and n1, n2, ... are the frequencies of the repeated letters.