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Worksheets11 Specialist Mathematics - Ch 7 Combinatorics
Total questions: 11
Worksheet time: 11mins
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
Each of the 30 students in a class studies French, German or Chinese. Of these students, 15 study French, 17 study German and 15 study Chinese. There are 15 students that study more than one subject. How many students study all three subjects?
2
3
4
5
6
