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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)