Permutations and Combinations

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 many ways can you arrange 3 books on a shelf?

Back

6 ways (3! = 3 × 2 × 1 = 6).

Front

If you have 5 different shirts and 4 different pants, how many outfits can you create?

Back

20 outfits (5 shirts × 4 pants = 20).

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

What is the formula for combinations of n objects taken r at a time?

Back

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

Front

How many different ways can you choose 2 fruits from a basket of 5?

Back

10 ways (C(5, 2) = 5! / [2!(5 - 2)!] = 10).

Front

What is a tree diagram?

Back

A tree diagram is a visual representation that shows all possible outcomes of a situation.

Front

If you flip a coin and roll a die, how many possible outcomes are there?

Back

12 outcomes (2 outcomes from the coin × 6 outcomes from the die = 12).

Front

In how many ways can you select 3 out of 6 candidates?

Back

20 ways (C(6, 3) = 6! / [3!(6 - 3)!] = 20).