Nov 13 - Combination

Front

What is a combination in mathematics?

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 selecting r items from n items?

Back

The number of combinations is calculated using the formula: 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 non-negative integer n, denoted as n!, is the product of all positive integers less than or equal to n.

Front

How many ways can you choose 3 city commissioners from 6 candidates?

Back

You can choose 3 city commissioners from 6 candidates in 20 ways, calculated as C(6, 3) = 6! / (3!(6 - 3)!) = 20.

Front

What is the difference between permutations and combinations?

Back

Permutations consider the order of selection, while combinations do not. For example, selecting A, B, C is different in permutations but the same in combinations.

Front

How many 2-digit numbers can be formed using the digits 1, 2, 3, and 4 without repetition?

Back

You can form 12 different 2-digit numbers using the digits 1, 2, 3, and 4 without repetition.

Front

What is the value of 12C4 + 12C3?

Back

The value of 12C4 + 12C3 is 715.

Front

How many different team combinations can be formed from 6 friends if each team has 3 players?

Back

You can form 20 different team combinations from 6 friends, calculated as C(6, 3) = 20.

Front

What is the formula for calculating permutations of n items taken r at a time?

Back

The formula for permutations is P(n, r) = n! / (n - r)!, where n is the total number of items and r is the number of items to arrange.

Front

How do you calculate the number of ways to arrange 8 trophies on a shelf?

Back

The number of ways to arrange 8 trophies is calculated using factorial: 8! = 40320.