11-22-24 Probability, Combinations, Permutations and Counting

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 taken r at a time?

Back

The formula is P(n, r) = n! / (n - r)!. Where n is the total number of objects and r is the number of objects to arrange.

Front

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

Back

The formula is 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 7! (7 factorial)?

Back

7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040.

Front

If a race has 25 participants and the top 8 advance, how many ways can the top 8 be chosen?

Back

The number of ways is given by permutations: P(25, 8) = 25! / (25 - 8)! = 1,081,575.

Front

What is the difference between permutations and combinations?

Back

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

Front

How many different arrangements can be made with the letters in the word 'CHAIR'?

Back

The number of arrangements is 5! = 120.

Front

What is the formula for calculating permutations of a set with repeated elements?

Back

The formula is P(n; n1, n2, ..., nk) = n! / (n1! * n2! * ... * nk!), where n is the total number of items and n1, n2, ..., nk are the counts of each repeated item.

Front

What is the significance of the binomial coefficient in combinations?

Back

The binomial coefficient C(n, r) represents the number of ways to choose r elements from a set of n elements without regard to the order.