Permutation, Combination, and Counting Principal

Front

What is a permutation?

Back

A permutation is an arrangement of objects in a specific order. The number of permutations of n distinct objects is n! (n factorial).

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 n! / (r!(n-r)!).

Front

What is the counting principle?

Back

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

Front

How many ways can you arrange 4 books on a shelf?

Back

24 ways (4! = 4 × 3 × 2 × 1 = 24).

Front

If a lock has 4 dials and each dial can have digits from 0 to 9 without repetition, how many combinations are possible?

Back

5040 combinations.

Front

How many ways can a student answer a multiple choice test with 15 questions and 5 options each?

Back

30,517,578,125 ways.

Front

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

Back

The formula is n! / (n-r)!.

Front

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

Back

The formula is n! / (r!(n-r)!).

Front

How many distinct arrangements can be made from the letters in the word 'OPPORTUNITIES'?

Back

389,188,800 distinct arrangements.

Front

If a restaurant offers 4 sizes of pizza, 2 types of crust, and 8 toppings, how many combinations of pizza with one topping are possible?

Back

64 combinations.