11 Specialist Mathematics - Ch 7 Combinatorics

Bao plans to study six subjects in Year 12. He has already chosen three subjects and for the remaining three he plans to choose one of four languages, one of three mathematics subjects and one of four science subjects. How many ways can he select his remaining subjects?

• 6

• 11

• 48

• 165

• 990

There are three flights directly from Melbourne to Brisbane. There are also two flights from Melbourne to Sydney and then four choices of connecting flight from Sydney to Brisbane. How many different paths are there from Melbourne to Brisbane?

• 9

• 11

• 18

• 20

• 24

In how many ways can 10 people be arranged in a queue at the bank?

• 10!

• 10¹⁰

• 2¹⁰

• ¹⁰C₂

• ¹⁰C₁

How many three-digit numbers can be formed using the digits 1, 2, 3, 4, 5 and 6 at most once?

• ⁶C₃

• 3!

• 6!

• 6 x 5 x 4

• 6 + 5 + 4

How many permutations of the word UTOPIA begin and end with a vowel?

• 90

• 288

• 384

• 720

• 4320

How many ways can four identical red flags and three identical blue flags be arranged in a row?

• 4 x 3

• 7! / (4! x 3!)

• 7! x 3! x 4!

• 4! x 3!

• 2! x 3! x 4!

How many ways can three DVDs be chosen from a collection of nine different DVDs?

• 3!

• 9 x 8 x 7

• ⁹C₃

• 9! / 3!

• 3 x 9

The number of subsets of {A,B,C,D,E,F} with at least one element is

• ⁶C₂

• ⁶C₂ - 1

• 2⁵ - 1

• 2⁶ - 1

• 2⁶

A class consists of nine girls and eight boys. How many ways can a group of two boys and two girls be chosen?

• 17! / (2! x 2!)

• ¹⁷C₄

• ⁹C₂ x ⁸C₂

• 17! / (9! x 8!)

• 9 x 8 x 8 x 7

There are six blue balls and five red balls in a bag. How many balls need to be selected at random before you are certain that three will have the same colour?

• 3

• 4

• 5

• 7

• 11