Permutation, Combination, and Counting Principal

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. It focuses on the group rather than the arrangement.

Front

How do you calculate the number of permutations of n objects taken r at a time?

Back

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

Front

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

Back

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

Front

What is the counting principle?

Back

The counting principle states that if one event can occur in m ways and a second can occur independently in n ways, then the two events can occur in m * n ways.

Front

Example of a permutation: Arranging 3 books on a shelf. How many ways can this be done?

Back

There are 6 ways to arrange 3 books (3! = 6).

Front

Example of a combination: Choosing 2 fruits from a basket of 5. How many combinations are possible?

Back

There are 10 combinations (C(5, 2) = 5! / (2! * 3!) = 10).

Front

What is the difference between permutation and combination?

Back

The key difference is that permutations consider the order of selection, while combinations do not.

Front

If a password consists of 4 digits, how many different passwords can be formed?

Back

There are 10,000 possible passwords (10^4 = 10,000).

Front

In how many ways can a committee of 4 be chosen from 10 students?

Back

There are 210 ways to choose the committee (C(10, 4) = 10! / (4! * 6!) = 210).