Mastering Permutations and Combinations

Front

What is a permutation?

Back

A permutation is an arrangement of objects in a specific order. The number of permutations of n distinct objects is given by n! (n factorial).

Front

What is a combination?

Back

A combination is a selection of objects without regard to the order. The number of combinations of n objects taken r at a time is given by the formula: C(n, r) = n! / (r!(n-r)!)

Front

How do you calculate the number of ways to choose r objects from n distinct objects?

Back

Use the combination formula: C(n, r) = n! / (r!(n-r)!)

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

In how many ways can a 4-member relay team be selected from a group of 8 athletes?

Back

70 (C(8, 4) = 8! / (4!(8-4)!) = 70).

Front

What is the probability of getting exactly two heads in four flips of a fair coin?

Back

The probability is \( \frac{3}{8} \) (Using the binomial probability formula).

Front

If a password is made by choosing three distinct letters from the alphabet, with letters being able to repeat, how many different passwords can be created?

Back

The number of different passwords is \( 26^3 \).

Front

What is the probability of selecting 3 red balls from a bag containing 5 red balls and 7 blue balls without replacement?

Back

The probability is \( \frac{10}{99} \).

Front

What is the difference between permutations and combinations?

Back

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

Front

What is the factorial of a number?

Back

The factorial of a non-negative integer n, denoted as n!, is the product of all positive integers less than or equal to n.