Permutation and Combination

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Across
  1. 1. There are 4 philosophy and 3 fiction books on the bookshelf. Philosophy books should be placed on the left side of the bookshelf and fiction books on the right side. How many ways are there to arrange the books?
  2. 2. A license plate begins with three letters. If the possible letters are C, A, T, C, and H, how many different permutations of the letters mentioned can be created if no letter is used more than once?
  3. 3. There are 5 men and 5 women in an office. A customer went in and requested a site visit from a group of 2 men and 3 women. How many different groups can be formed from the office?
  4. 5. A basketball team has 12 players, there are always basketball players on the court. How many different groups of players can play on the court at any one time?
  5. 9. If an elementary class has 13 students, how many different arrangements can 6 students give a presentation to the class?
  6. 11. In how many ways can the letters in the word MISSISSIPPI be arranged if the P's are together?
  7. 13. There are 15 players in a game at a birthday party, players should be taken 3 at a time. In how many ways can the host choose the players?
  8. 14. 7 fruits can be put in a salad but only 4 can be chosen. How many ways can we do this
  9. 15. A permutation lock will open if the right choice of 3 numbers (from 1 to 20) is selected. How many lock permutations can be made assuming no number is repeated?
  10. 17. A museum has 8 sculptures made by Michelangelo and wants to arrange 5 of them on the same wall. In how many ways are there to arrange the sculptures?
  11. 18. In how many ways can the letter of the word CRINGE be arranged?
  12. 20. There are 2 girls and 4 boys in a pictorial. They are supposed to sit in a line where the 2 girls are on the ends. How many different ways can they be arranged?
  13. 21. How many different linear arrangements of the letters from the word PIZZERIA can be created?
  14. 22. A set containing 7 elements which are N, E, T, W, O, R, and K. In how many different ways can 3 elements be selected out of the total number of elements without repetition?
  15. 23. There are 12 points selected on a circle. How many triangles with edges in these points exist?
Down
  1. 1. In how many ways can you arrange 4 green balls, 3 red balls, and 2 pink balls? Take note that the balls of the same color are identical.
  2. 3. There are 4 girls and 5 boys in a class, these students are assigned to sit in a line. However, the 4 girls chose to always sit together. In how many different ways can they be arranged?
  3. 4. In how many ways can you arrange the letters from the word LOLLIPOP?
  4. 5. In how many ways can a president, a vice president, and a secretary be chosen from among 10 candidates?
  5. 6. A kpop group has 9 options of songs, but they only have to perform 3 of them. How many different ways can they do this (the order matters)?
  6. 7. In a shop, there is a set of 5 candies. In how many ways can 2 candies be selected from the set without repetition?
  7. 8. A customer buys a family-sized meal at a certain restaurant, he gets to choose 3 side dishes from 9 options. The customer is going to choose 3 different side dishes. How many ways can he possibly group the 3 side dishes?
  8. 10. In how many ways can the letters of the word MATHEMATICS be arranged?
  9. 11. How many combinations can the 7 colors of the rainbow be grouped into groups of 3 colors each?
  10. 12. In how many ways can the letters from the word BALLS be arranged if the L's are together?
  11. 14. A horse race has 16 horses. How many different ways can the 1st, 2nd, and 3rd place occur (the order matters)?
  12. 16. How many committees of 4 can be created from a group of 20 students?
  13. 17. In how many ways can 5 children, and three of them are always together be arranged in a line?
  14. 19. How many different ways can 4 cards be dealt from a deck of 52 cards?