Problems with solutions

1. How many 4 digit numbers can we make using the digits 3, 6, 7 and 8 without repetitions?
   
   
2. How many 3 digit numbers can we make using the digits 2, 3, 4, 5, and 6 without repetitions?
   
   
3. How many 6 letter words can we make using the letters in the word LIBERTY without repetitions?
   
   
4. In how many ways can you arrange 5 different books on a shelf?
   
   
5. In how many ways can you select a committee of 3 students out of 10 students?
   
   
6. How many triangles can you make using 6 non collinear points on a plane?
   
   
7. A committe including 3 boys and 4 girls is to be formed from a group of 10 boys and 12 girls. How many different committee can be formed from the group?
   
   
8. In a certain country, the car number plate is formed by 4 digits from the digits 1, 2, 3, 4, 5, 6, 7, 8 and 9 followed by 3 letters from the alphabet. How many number plates can be formed?

Solutions

1. 4! = 24
   
   
2. ₅ P ₃ = 60
   
   
3. ₇ P ₆ = 5040
   
   
4. 5! = 120
   
   
5. ₁₀ C ₃ = 120
   
   
6. ₆ C ₃ = 20
   
   
7. ₁₀ C ₃ * ₁₂ c ₄ = 59,400
   
   
8. ₉ P ₄ * ₂₄ P ₃ = 36,723,456