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Discrete Mathematics

Rule of Sum and Rule of Product

Rule of Sum and Rule of Product Problem Solving


Aleasha has a standard 6-sided die and a coin. If she chooses one of them and then rolls or flips it, how many different results can she get?

There are \(8\) cards with number \(10\) on them, \(5\) cards with number \(100\) on them and \(2\) cards with number \(500\) on them. How many distinct sums are possible using from 1 to all of the \(15\) cards?

Paddy flips a fair coin \(6\) times, and writes down each result in order. What is the total number of possible outcomes?

Note: The outcome \(THHH\) is different from the outcome \(HHHT\).

How many ways are there to color the above regions with 4 different colors, if adjacent regions should have different colors?

Note: You need not use all four colors but each region must be colored by any one of them.

How many odd 3-digit numbers are there, whose digits are distinct integers from the set \( \{0, 1, 2, 3, 4, 5, 6, 7 \} \).

This problem is posed by Gabriel M.

Details and assumptions

The number \(12=012\) is a 2-digit number, not a 3-digit number.


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