Probability with Combinations

Front

What is a combination in probability?

Back

A combination is a selection of items from a larger set where the order of selection does not matter.

Front

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

Back

The formula is C(n, r) = n! / (r!(n - r)!), where n is the total number of items, r is the number of items to choose, and ! denotes factorial.

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 up to n.

Front

What is the difference between permutations and combinations?

Back

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

Front

How many different license plates can be formed with the first letter Q, the second letter M or N, the third letter B, P, or D, and the first digit 0?

Back

600 possible license plates.

Front

How many ways can you choose 2 meats from 15 options?

Back

C(15, 2) = 105 ways.

Front

How many ways can you choose 3 veggies from 20 options?

Back

C(20, 3) = 1,140 ways.

Front

What is the total number of different pizzas that can be formed with one size, one crust, 2 meats, and 3 veggies?

Back

1,436,400 different pizzas.

Front

What is the probability of Shellie being assigned the PIN 1234 if the first digit is 0 or 1 and no digit can repeat?

Back

1/672.

Front

What is the probability that at least one of the winners is a boy in a drawing with 15 boys and 15 girls for 4 tickets?

Back

248/261.