Counting Principle, Combination, Permutation Practice

Front

What is the Counting Principle?

Back

The Counting Principle states that if there are 'm' ways to do one thing and 'n' ways to do another, then there are m × n ways to do both.

Front

Define 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 n! / (n - r)!.

Front

Define Combination.

Back

A combination is a selection of items from a larger set where the order does not matter. The number of combinations of 'n' items taken 'r' at a time is given by n! / (r!(n - r)!).

Front

How many different plans can you choose if you have 10 phones, 6 calling plans, and 3 texting plans?

Back

180 (10 × 6 × 3 = 180).

Front

How many ways can 3 contestants be selected from 10 contestants?

Back

120 (10C3 = 10! / (3!(10 - 3)!) = 120).

Front

How many different arrangements can be made from 10 contestants for 3 prizes?

Back

720 (10P3 = 10! / (10 - 3)! = 720).

Front

How many different iPhone combinations exist with 3 models, 4 colors, and 3 storage options?

Back

36 (3 × 4 × 3 = 36).

Front

How many ways can 7 songs be arranged from a selection of 12 songs?

Back

792 (12P7 = 12! / (12 - 7)! = 792).

Front

What is the formula for calculating permutations?

Back

The formula for permutations is nPr = n! / (n - r)!.

Front

What is the formula for calculating combinations?

Back

The formula for combinations is nCr = n! / (r!(n - r)!).