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Rule of Sum and Rule of Product

Seek simple and succinct solutions in these systems by sussing-out the significant symmetries.

Rule of Product

Calvin stays on the 7th floor in his building. Between each floor, there are exactly 12 stairs. If he starts from the 1st floor and climbs his way up to the 7th floor, how many stairs does he climb?

Bernie's Breakfast Buffet has a wide selection of breakfast food available. They have \(8\) types of cereal, \(6\) types of fruit, and \(6\) styles of cooked eggs. How many different ways can someone choose a breakfast consisting of one type of cereal, one piece of fruit, and one style of cooked eggs?

A soccer team has t-shirts in \(7\) different colors and pants in \(9\) different colors. What is the total number of different uniform color combinations for the team?

A palindrome is a number that reads the same forwards as it does backwards. For example, 98789 is a 5-digit palindrome, and 7337 is a 4-digit palindrome. How many 3-digit palindromes are there?

While training for a triathlon, Trina will first swim, then cycle and finally run. She will swim either 200, 300, 400 or 500 metres, followed by cycling 5, 9, or 13 kilometres, and finally running either 2 or 3 kilometres. How many different possible choices of training routines does Trina have?

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