Paper 2 Section B Practice: Permutations and Combinations

Original practice material

These questions total 24 marks. State enough structure to show that every valid outcome is counted exactly once.

Answers: Permutations and Combinations Answers.

Question 1: codes with restrictions

A code contains three different letters chosen from $A,B,C,D,E,F$, followed by two different digits chosen from $0,1,2,3,4$. The first letter must be a vowel, where the vowels available are $A$ and $E$, and the first digit cannot be $0$.

Find the number of possible codes. [4]

Question 2: committee selection

A committee of 5 is chosen from 7 students and 4 teachers.

(a) Find the number of committees containing exactly 2 teachers. [2]

(b) Find the number of committees containing at least 1 teacher. [3]

(c) Two of the students, Jia and Noor, will not serve together. Find the number of committees containing exactly 2 teachers and not containing both Jia and Noor. [4]

Question 3: repeated letters with a positional restriction

Find the number of distinct arrangements of the letters in STATISTICS for which the three letters $S$ are not all consecutive. [5]

Question 4: circular arrangements

Seven students, including Ali and Bea, sit around an unnumbered circular table.

(a) Find the number of arrangements if Ali and Bea must sit next to each other. [2]

(b) Find the number of arrangements if Ali and Bea must not sit next to each other. [2]

(c) Another student, Chen, must sit between Ali and Bea, adjacent to both. Find the number of arrangements. [2]