Combinations

Front

What is a combination?

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 combinations?

Back

The number of combinations of n items taken k at a time is calculated using the formula: C(n, k) = n! / (k!(n-k)!), where n! is the factorial of n.

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

If a committee of 5 is to be formed from 12 students, how many ways can this be done?

Back

C(12, 5) = 12! / (5!(12-5)!) = 792.

Front

If Paul must be on the committee, how many ways can the rest be chosen?

Back

If Paul is included, we choose 4 more from the remaining 11 students: C(11, 4) = 330.

Front

How many lines can be drawn from 17 points on a circle?

Back

The number of lines is given by C(17, 2) = 136.

Front

What is the maximum number of boys in a committee of 5 from 8 boys and 9 girls?

Back

The maximum number of boys is 5.

Front

How do you calculate the number of committees with at most 2 boys?

Back

Calculate the number of committees with 0, 1, and 2 boys separately and sum them.

Front

How many different pizzas can be made with 4 toppings including pepperoni from 9 options?

Back

Choose 3 from the remaining 8 toppings: C(8, 3) = 56.

Front

How many sandwiches can be made with 3 meats from 6 and 5 veggies from 10?

Back

C(6, 3) * C(10, 5) = 20 * 252 = 5,040.