4.7 – Solving Counting Problems Worksheet
Name:_________________________
Total:
Reminder to use:
Fundamental Counting Principle – if multiple tasks or stages are linked by the word “and”, lining up,
order matters, using cases or specifics.
Repetition – if there is a repetition then you must divide by r!
Permutations – When there are not cases or specifics, order matters, appointing specific jobs
Combinations – Order doesn’t matter, not appointing specific jobs.
1.
How many sequences can be formed using each of the digits 0 through 9 exactly once, if:
 The final digit in the sequence is 0
 A multiple of 4 is the first digit in the sequence, and
 Another multiple of 4 is either 5th, 6th or 7th in the sequence.
Use cases. (3 marks)
2.
How many different 4-card hands containing at least 1 heart can be dealt to one person from a
standard deck or playing cards? (2 marks)
3. How many possibilities are there for a five-digit combination using the digits from 0 to 9?
a. If each digit can be used many times? (1 mark)
b. If each digit can be used only once? (1 mark)
4. Keith is creating a collage using 6 separate prints of an image of Mt. Robson, Brinish Columbia,
each print in a different monochrome colour. How many collages using at least 4 of the prints
can Keith create? (2 marks)
5. How many unordered collections of 3 letters and 4 digits are possible if no characters are
repeated? (1 mark)