FAD1015: Mathematics III — Tutorial 2

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

Topic: Combination

Question 1

Find the value of $n$.

(a) $_nC_6 = ,_nC_3$

(b) $_nC_2 = 28$

(c) $_{n+1}C_3 = 4 \times ,_nC_2$

Question 2

A team of 5 students is to be chosen from a class of 12 boys and 9 girls. In how many ways can a team be chosen if they consists of:

(a) 3 boys and 2 girls,

(b) 3 girls and 2 boys,

(c) at least 3 girls?

Question 3

A five member committee of debating team is formed from 6 students, 2 lecturers and one officer. How many ways can the committee are formed if:

(a) the officer must be in the committee,

(b) exactly 4 students are chosen,

(c) not more than 4 students are chosen

Question 4

Given that 6 out of 20 PASUM students are chosen at random to be part of the Jogathon committee.

(a) How many ways can the committee be chosen?

(b) How many ways can the committee be chosen if two particular students are decided to be in the committee?

Related Concepts

  • Combination — selection of objects where order does not matter
  • Binomial Coefficient — $_nC_r$ notation
  • Combinatorics — branch of mathematics dealing with counting

Source: FAD1015 Questions T1-T6 _20252026.pdf