Probability - Combinations

Front

What is the formula for combinations?

Back

The formula for combinations 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

Calculate ₁₅C₂.

Back

₁₅C₂ = 105.

Front

What does _nC_r represent in probability?

Back

_nC_r represents the number of ways to choose r items from n items without regard to the order of selection.

Front

How many ways can 4 paintings be chosen from 25?

Back

There are 12,650 ways to choose 4 paintings from 25.

Front

What is the difference between permutations and combinations?

Back

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

Front

Calculate ₁₂C₃.

Back

₁₂C₃ = 220.

Front

If 15 people are running a race, how many ways can the top 5 finishers be selected?

Back

There are 3,003 ways to select the top 5 finishers from 15 people.

Front

How many ways can 8 cheerleaders be chosen for 3 positions?

Back

There are 56 ways to choose 3 positions from 8 cheerleaders.

Front

What is a factorial?

Back

A factorial, denoted as n!, is the product of all positive integers up to n.

Front

What is the significance of the combination formula in real-life scenarios?

Back

The combination formula is used in various fields such as statistics, finance, and event planning to determine possible selections.