Counting Methods

Front

What is the fundamental principle of counting?

Back

The fundamental principle of counting 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 choices do you have for the first digit of a 4-digit number if it cannot be 0?

Back

You have 9 choices (1-9) for the first digit.

Front

If repetition is allowed, how many 4-digit numbers can be formed?

Back

9,000 (9 choices for the first digit and 10 choices for each of the remaining 3 digits: 9 × 10 × 10 × 10 = 9,000).

Front

If repetition is not allowed, how many 4-digit numbers can be formed?

Back

4,536 (9 choices for the first digit, 9 for the second, 8 for the third, and 7 for the fourth: 9 × 9 × 8 × 7 = 4,536).

Front

What is a combination in counting methods?

Back

A combination is a selection of items from a larger set where the order does not matter.

Front

What is a permutation in counting methods?

Back

A permutation is an arrangement of items where the order does matter.

Front

How many different pizzas can you make with 3 crust options, 5 sauce options, and 10 topping options?

Back

150 (3 × 5 × 10 = 150).

Front

How do you calculate combinations?

Back

Combinations are calculated using the formula C(n, r) = n! / (r!(n - r)!), where n is the total number of items, and r is the number of items to choose.

Front

How do you calculate permutations?

Back

Permutations are calculated using the formula P(n, r) = n! / (n - r)!, where n is the total number of items, and r is the number of items to arrange.

Front

In a coed volleyball team with 7 boys and 5 girls, how many ways can you select 3 boys and 3 girls?

Back

350 (C(7, 3) × C(5, 3) = 35 × 10 = 350).