combinations

Twelve students tried out for the football team. Coach Moorhead only has 5 openings. In how many ways, can he pick 5 of the 12 students to be on the team? We use the combinations formula. We can write this as 12C5. Type this into our search engine and we get: 792 ways

a licence plate that has 3 numbers from 0 to 9 followed by 2 letters How many license plate combinations can we form? We multiply as follows: [0-9] = 10 possible digits (D) A-Z = 26 possible letters (L) The problem asks for this: DDDLL So we have: 10 * 10 * 10 * 26 * 26 = 676,000 plates

From a group of 10 men and 8 women, how many ways can 2 men and 3 women be chosen for 5 positions? We use combinations. Since men and women are independent, we multiply each result: We want 10 men choose 2 men multiplied by 8 women choose 3 women. Type 10C2 into our search engine and we get 45...

A pollster selected 4 of 7 people. How many different groups of 4 are possible? We want to use the combinations formula. So we type 7C4 into our search engine. This is also known as 7 choose 4. We get 35 different groups.

A catering service offers 3 appetizers, 6 main courses, and 4 desserts. A customer is to select 2 appetizers, 3 main courses, and 3 desserts for a banquet. In how many ways can this be done? We use the combinations formula, and since each event is independent of the others, we multiply: 2...

Committees of 4 men 5 women form a group of 11 men and 11 women. We want combinations. 4 men from 11 men is the combination 11C4. Using our combinations calculator, we get: 11C4 = 330 5 women from 11 women is the combination 11C5. Using our combinations calculator, we get: 11C5 = 462 We...

A committee consisting of 4 faculty members and 5 students is to be formed. Every committee position has the same duties and voting rights. There are 12 faculty members and 15 students eligible to serve on the committee. In how many ways can the committee be formed? We'll use combinations, so...

A catering service offers 4 appetizers, 12 main courses, and 9 desserts. A customer is to select 3 appetizers, 10 main courses, and 5 desserts for a banquet. In how many ways can this be done? We use combinations, so we have: 4C3 appetizers = 4 12C10 main courses = 66 9C5 desserts = 126 We...

A license plate is made up of 2 letter and 3 single digit numbers. There are 26 letters (A-Z). And there are 10 single digit numbers [0-9]. So our total combinations are: Letter - Letter - Number - Number - Number 26 * 26 * 10 * 10 * 10 = 676,000

From 9 names on a ballot, a committee of 4 will be elected to attend a political national convention. How many different committees are possible? A. 3024 B. 15,120 C. 1512 D. 126 We want unique combinations, so we have 9 choose 4, or 9C4. Typing this into the search engine, we get: 9C4 = 126...

Evaluate the expression (8C3) (7C6) 8C3 = 56 7C6 = 7 (8C3) (7C6) = 56 * 7 (8C3) (7C6) = 392

A restaurant has 8 pizza toppings to choose from. How many different 2 topping pizzas are possible? We want 8 combinations of 2, denoted as 8 C 2, or 8 choose 2. Typing 8 C 2 into the search engine, we get 28 different 2 topping pizzas

A school dance committee is to consist of 2 freshmen, 3 sophomores, 4 juniors, and 5 seniors. If 6 freshmen, 9 sophomores, 7 juniors, and 7 seniors are eligible to be on the committee, in how many ways can the committee be chosen? We want combinations for freshmen, sophomores, juniors, and...

If there are 8 girls entered in a race, how many different ways can the runners place first, second, and third? We want 8 choose 3, or 8C3. Type 8C3 into the search engine, and we get 56 different ways to place first, second, and third.

A restaurant offers a special pizza with any 5 toppings. If the restaurant has 17 topping from which to choose, how many different special pizzas are possible? We have 17 choose 5, or 17C5. Type this into the search engine, and we get 6,188 different special pizzas available.

A local college classifies its students by major, year (Freshman, Sophomore, Junior, Senior) and sex (M, F). If the college offers 20 majors, how many combinations are possible? We have 20 majors, 4 grade levels, and 2 sexes. The total combinations = 20 * 4 * 2 = 160

Tony has 6 cds that he is giving away. He lets his best friend choose 3 of the 6 cds. How many groups of 3 cds are possible? This problem asks for unique combinations. We want 6 choose 3, or 6C3. Go to the search engine, and type in 6C3, we get 20 possible groups.

Chris has 6 cds that he is going to give away. He let his best friend choose 2 of the 6 cds. How many different groups of 2cds are possible? We want 6 choose 2 using combinations. We use combinations because the problem states the word different. 6 C 2 using our calculator is 15.

A 3-digit security code can use the numbers 0-9. How many possible combinations are there if the numbers can be repeated [0-9] * [0-9] * [0-9] 10 * 10 * 10 = 1,000 combinations

To create an entry code, you must first choose 2 letters and then, 4 single-digit numbers. How many different entry codes can you create? List total combinations using the product of all possibilities: 26 letters (A - Z) * 26 letters (A - Z) * 10 digits (0-9) * 10 digits (0-9) * 10 digits (0-9)...