Permutation or Combination

Front

What is a permutation?

Back

A permutation is an arrangement of objects in a specific order. The order matters in permutations.

Front

What is a combination?

Back

A combination is a selection of objects where the order does not matter.

Front

In how many ways can 3 runners finish in 1st, 2nd, and 3rd place in a race?

Back

This is a permutation problem. The number of ways is calculated as 3! = 6.

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

If a keylock has 4 digits, how many different codes can be formed if the order of digits matters?

Back

This is a permutation problem. If digits can repeat, there are 10^4 = 10,000 possible codes.

Front

How many ways can 3 members be selected for President, Vice President, and Treasurer from a group of 5?

Back

This is a permutation problem. The number of ways is P(5, 3) = 5! / (5 - 3)! = 60.

Front

What is the difference between permutations and combinations?

Back

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

Front

If a DJ has 9 songs and needs to arrange 3, how many arrangements are possible?

Back

This is a permutation problem. The number of arrangements is P(9, 3) = 9! / (9 - 3)! = 504.

Front

Can you give an example of a situation where combinations are used?

Back

Choosing 3 toppings from a list of 10 for a pizza, where the order of toppings does not matter.

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.