Computational Mathmatics
Victorian Institute of Technology Pty Ltd
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ITSU2011 – Computational Mathematics Page 1 of 3
ITSU2011
Computational Mathematics
Activity 04
Victorian Institute of Technology Pty Ltd
ABN: 41 085 128 525 RTO No: 20829 TEQSA ID: PRV14007 CRICOS Provider Code: 02044E
ITSU2011 – Computational Mathematics Page 2 of 3
Q1) How many permutations of 3 different digits are there, chosen from the ten digits 0 to 9
inclusive?
(Such as drawing ten numbered marbles from a bag, without replacement)
Q2) How many permutations of 4 different letters are there, chosen from the twenty six letters of
the alphabet?
Q3) How many different committees of 5 people can be chosen from 10 people?
Q4) Jones is the Chairman of a committee. In how many ways can a committee of 5 be chosen
from 10 people given that Jones must be one of them?
Q5) A special type of password consists of four different letters of the alphabet, where each letter
is used only once. How many different possible passwords are there?
Q6) A password consists of two letters of the alphabet followed by three digits chosen from 0 to
9. Repeats are allowed. How many different possible passwords are there?
Q7) An encyclopedia has eight volumes. In how many ways can the eight volumes be replaced
on the shelf?
Q8) Assuming that any arrangement of letters forms a 'word', how many 'words' of any length
can be formed from the letters of the word SQUARE? (No repeating of letters).
Q9) 16 teams enter a competition. They are divided up into four Pools (A, B, C and D) of four
teams each.
Every team plays one match against the other teams in its Pool.
After the Pool matches are completed:
• the winner of Pool A plays the second placed team of Pool B
• the winner of Pool B plays the second placed team of Pool A
• the winner of Pool C plays the second placed team of Pool D
• the winner of Pool D plays the second placed team of Pool C
The winners of these four matches then play semi-finals, and the winners of the semi-finals play
in the final.
Victorian Institute of Technology Pty Ltd
ABN: 41 085 128 525 RTO No: 20829 TEQSA ID: PRV14007 CRICOS Provider Code: 02044E
ITSU2011 – Computational Mathematics Page 3 of 3
How many matches are played altogether?
Q10) A restaurant offers 5 choices of appetizer, 10 choices of main meal and 4 choices of
dessert. A customer can choose to eat just one course, or two different courses, or all three
courses. Assuming all choices are available, how many different possible meals does the
restaurant offer?