combinations

A restaurant offers the following options: Starter – soup or salad Main – chicken, fish or vegetarian Dessert – ice cream or cake How many possible different combinations of starter, main and dessert are there? Using the fundamental rule of counting, we have: 2 starters * 3 main courses * 2...

The formula is nC2 - rC2 + 1 In this problem: n = 8 and r = 3 8C2 = 28 3C2 = 3 Evaluating, we have: 28 - 3 + 1 26

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One thousand people in. room decide to shake hands with every other person in the room. Instead of one handshake per couple, each person must shake both of the hands of every person in the room with both his right and his left hand. (Tom will use his right hand to shake Dave's right hand and...

If 100 people are required to introduce themselves to each other and shake hands with each person one time, how many handshakes will take place? We want 100 choose 2 since we have 2 people per handshake: 100C2 = 4950

Five players are going to be picked to start a basketball game. If there are 13 players on the team, how many different combinations of 5 starting players can be made? We want 13 combinations of 5 13C5 = 1287

Eight people have volunteered for a secret mission that requires only 3 people. How many different combinations are possible? We want 8 combinations of 3 8C3 = 56

A music camp with 50 students decided to break the students into barbershop quartets to see which combination of four students sounded the best. How many different barbershop quartets can be made with 50 students so that each possible combinations of four is tried? We want 50 combinations of 4...

Mrs. Lopez gave a homework assignment over summer vacation to read three books from the following list: a) Call of the Wild b) Wuthering Heights c) Death of a Salesman d) The Cartoon Book of Physics How many possible combinations of three books are there in the list of four books? We need to...

Dale has a box that contains 20 American quarters and 20 Canadian quarters. If he takes them from the box one at a time, how many must he remove before he is guaranteed to have 5 quarters from the same country? Worst case scenario, Dale picks 4 American and 4 Canadian quarters which guarantees...

THE PLAYER CHOSE 20 OUT OF 70 NUMBERS IN A GAME OF CHANCE. ...WHEN THE SHOW BEGIN,THE BANKER WILL THEN RAFFLE OR DO A DRAW WHERE IN THE BANKER PICKS AS WELL 20 OUT OF 70 NUMBERS. .....NOW HERES THE TRICK, FOR YOU TO BEAT THE BANKER .YOUR CHOSEN 20 NUMBERS SHOULD NOT MATCH ANY OF THE BANKER...

There are 24 competitors in a cycling race. How many different selections are possible for first and second place? We want unique combinations, so we have: 24 C 2 = 276

11 combination of 3 times 6 combination of 3 11 combination of 3 = 165 6 combination of 3 = 20 11 combination of 3 times 6 combination of 3 = 165 * 20 11 combination of 3 times 6 combination of 3 = 3300

How many ways can a basketball coach choose to the first five player from a group of 15 players We use combinations. We want 15 choose 5. We type this in our search engine and we get: 15C5 = 3,003 different five player rosters

a license plate has 3 letters followed by 4 numbers There are 26 letters A-Z and 10 numbers 0-9. So we have: 26 * 26 * 26 * 10 * 10 * 10 * 10 175,760,000 different license plate combinations

Suppose you are asked to choose three movies. If there are 20 different movies, in how many ways can the three movies be chosen? We want unique combinations, so we have 20 choose 3: We type 20C3 into our search engine and we get: 20C3 = 1,140

How many 4 person committees can be formed from a group of 11 people We want 11 choose 4, or 11C4. We type 11C4 into our search engine and we get: 330 committees

A bag contains 8 marbles of different colors. How many ways unique ways or orders can you select 3 marbles? We want the combinations formula, 8 choose 3, or 8C3. Type 8 C 3 into our search engine and we get: 56 unique ways

Meryl can only take 4 out of 7 classes offered during the summer. How many different ways can she choose the classes she will take We want 7 choose 4, or 7C4: We type 7C4 into our search engine and we get: 35

A committee of 6 students are being selected from a class of 10 girls and 8 boys. How many committees are possible if three must be girls and 3 must be boys? We want combinations. How many ways can we choose 3 boys from 8 boys: 8 choose 3 = 56 We want combinations. How many ways can we choose...