Worksheet Chapter 4: Permutation and Combination

1. State whether the following statement is True or False: 'The number of permutations of n distinct objects is always greater than or equal to the number of combinations of choosing r objects from those n objects (where r ≤ n).'

2. There are 12 points marked on a circumference of a circle. (a) Find the number of chords that can be drawn using any two points. (b) Find the number of triangles that can be formed using any three points as vertices.

3. Calculate the value of 7! - 5!5!.

4. A school debate team of 5 members is to be formed from 6 prefects and 4 class monitors. Calculate the number of different ways to form the team such that it contains (a) exactly 3 prefects, (b) at most 1 class monitor.

5. Find the number of distinct arrangements of all the letters in the word 'PARALLEL'.

6. Fill in the blank: The number of distinct arrangements of n objects placed around a circular table is given by the formula (________)!.

7. Find the value of n if (n + 1)P3 = 12 × nP2.

8. Seven people including a couple, Mr. and Mrs. Lee, are to be seated in a row of 7 chairs. Calculate the number of possible seating arrangements if (a) Mr. and Mrs. Lee must sit next to each other, (b) Mr. and Mrs. Lee refuse to sit next to each other.

9. A sports coach needs to select 5 players from a squad of 11 players. Which expression represents the total number of ways the coach can make this selection?

10. Four-digit passcode numbers are to be formed using the digits 2, 3, 5, 7, 8, and 9 without repetition. (a) How many passcodes can be formed in total? (b) How many of these passcodes are greater than 5000?