FAD1015: Mathematics III — Tutorial 1

Centre for Foundation Studies in Science
Universiti Malaya
Session 2025/2026

Topic: Counting and Permutation

Question 1

Without using a calculator, evaluate ${n}P{r-1}$ and $_nP_r$.

Question 2

In a pet competition, in how many ways can the organiser arrange 3 dogs and 5 cats in a row such that the dogs must be separated?

Question 3

Find the number of ways in which all ten letters of the word MOTIVATION can be arranged if:

(a) if there is no restriction,

(b) if the arrangement must be end with V,

(c) if two letters T must be placed next to each other,

(d) if two letters O must not be placed next to each other,

(e) if the arrangements starts with A and end with I.

Question 4

Eight different beads are formed into a ring. How many different ways are there?

Question 5

In how many ways can 5 people sit in a round table if:

(a) they can sit anywhere

(b) 2 particular people must not sit next to each other?

Question 6

Consider the digits from 1, 2, 3, …, 9. In how many ways four digits numbers can be formed if:

(a) they can only be used once?

(b) repetitions are allowed?

(c) the numbers are even?

(d) they are greater than 6000?

(e) they are between 2000 and 8000 and repetitions are allowed?

Related Concepts

  • Permutation — arrangement of objects where order matters
  • Circular Permutation — arranging objects in a circle
  • Factorial — mathematical operation used in counting
  • Combinatorics — branch of mathematics dealing with counting

Source: FAD1015 Questions T1-T6 _20252026.pdf