Counting Principles, Permutations, and Combinations Practice Problems

Five-digit even numbers greater than 90000 can be formed by using the digits 2, 3, 4, 5, 6, and 9. State the number of such numbers.

Use the combination formula to solve the following problem.

A class has 50 students. If the teacher needs to select 8 students to attend the science exhibit, how many groups of 8 students are possible?

Use the combination formula to solve the following problem.

You are planning to take two electives for this upcoming semester. If there are 12 offered electives, how many possible sets of two electives can you take?

Use the combination formula to solve the following problem.

You have 15 different seeds available. If you are only going to plant 4 seeds, how many possible sets of 4 seeds can you plant?

Use the combination formula to solve the following problem.

A band was invited to perform in an event. If they are going to select three songs from their album which has twelve songs, determine how many ways the selection be done.

Use the Fundamental Counting Principle to solve the following problem.

A shop sells their shirt in three different sizes (small, medium, and large), four types (polo, sleeveless, crew neck, and v-neck), and five colors (gray, blue, black, red, and pink). Determine how many ways a shirt can be bought.

Use the Fundamental Counting Principle to solve the following problem.

A furniture store sells their table in three different materials (plastic, wood, or metal) and in four different lengths (3 ft, 4 ft, 5 ft, or 6 ft). Determine how many choices of tables a customer has.

Use the Fundamental Counting Principle to solve the following problem.

A meal has five choices for the main dish and four choices for the beverage. Determine how many ways the meal can be ordered.

Evaluate the following expression: (₆C₄ x ₉C₁)/₁₂C₄

Evaluate the following expression: ₆C₂/₆C₄ - 120!/118!

Evaluate the following expression: 3 - ₅P₂/₆P₅

Evaluate the following expression: ₈P₄/4! + ₈C₄

Using the formula for _nC_r, solve the following expression.

₁₁C₀

Using the formula for _nC_r, solve the following expression.

₁₅C₁₅

Using the formula for _nC_r, solve the following expression.

₁₃C₆

Using the formula for _nP_r, solve the following expression.

₂₄P₀

Using the formula for _nP_r, solve the following expression.

₄P₄

Using the formula for _nP_r, solve the following expression.

₆P₃

Using the formula for _nP_r, solve the following expression.

₁₁P₂

Seven customers are in queue in a cafeteria. In how many ways can these people be lined up? 

In how many different ways can John select 4 shirts from his 11 shirts for his upcoming vacation?

A set of 12 students participated in a drawing competition which has a first, second, and third prize. In how many ways can these prizes be won?

Evaluate the following permutation: ₁₄P₃

Evaluate the following permutation: ₁₀P₂

Using the formula for _nC_r, solve the following expression.

₇C₃

Using the formula for _nP_r, solve the following expression.

₉P₅

Using the formula for _nP_r, solve the following expression.

₈P₂

Using the formula for _nP_r, solve the following expression.

₃P₃

Using the formula for _nC_r, solve the following expression.

₁₂C₈

Using the formula for _nC_r, solve the following expression.

₁₂C₁₂

Using the formula for _nC_r, solve the following expression.

₂₂C₀