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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 Problem Solving

Hiro went to the store after school to pick up one jug of milk, one loaf of bread, one dozen eggs and one package of cookies. Milk comes in 1%, 2% and 3.25% varieties. Bread comes in white and 100% whole wheat. Eggs come in dozen-pack of various sized: small, medium, large and jumbo. Cookies come in three different flavours. How many different ways can Hiro bring home the items from his list?

How many 3-digit even numbers are there, which comprise of the digits 1, 2 and 3 in some order?

How many ways are there to elect one president and one vice president from \(25\) candidates?

Details and assumptions

The president and vice president cannot be the same person.

How many ways are there to color the above regions with 3 different colors, if adjacent regions should have different colors?

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

In Alice's closet, there are \(4\) different pants, \(9\) different shirts and \(n\) different jackets. If the number of combinations of pants, shirts and jackets Alice can choose is \(252,\) how many different jackets does she have?

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