Mastering Permutations and Combinations

Front

What is a permutation?

Back

A permutation is an arrangement of objects in a specific order. The number of permutations of n objects taken r at a time is given by the formula P(n, r) = n! / (n - r)!.

Front

What is a combination?

Back

A combination is a selection of objects without regard to the order. The number of combinations of n objects taken r at a time is given by the formula C(n, r) = n! / [r!(n - r)!].

Front

How do you calculate the number of ways to arrange r objects from n distinct objects?

Back

Use the permutation formula: P(n, r) = n! / (n - r)!.

Front

What is the value of 5! (5 factorial)?

Back

5! = 5 × 4 × 3 × 2 × 1 = 120.

Front

If n = 8 and r = 3, what is P(n, r)?

Back

P(8, 3) = 8! / (8 - 3)! = 8 × 7 × 6 = 336.

Front

How many different 3-digit codes can be created if no digit repeats?

Back

The number of different codes is calculated as P(10, 3) = 10 × 9 × 8 = 720.

Front

What is the formula for calculating combinations?

Back

C(n, r) = n! / [r!(n - r)!].

Front

What is the difference between permutations and combinations?

Back

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

Front

Calculate the number of ways to seat 3 students in a row of 5 chairs.

Back

The number of ways is P(5, 3) = 5! / (5 - 3)! = 5 × 4 × 3 = 60.

Front

If n = 7 and r = 5, what is P(n, r)?

Back

P(7, 5) = 7! / (7 - 5)! = 7 × 6 × 5 × 4 × 3 = 2,520.