There are 
ways for the teacher to decide which student she will teach during each lesson time if she must teach each student exactly 3 times. Here, "!" represents the factorial.
A number's factorial is the result of multiplying the integer by each natural number below it. Factorial can be symbolized by the letter "!". Thus, n factorial is denoted by n! and is the result of the first n natural numbers.
A whole number's "n" factororial is the sum of that number and each whole number up to one.
When a question asks you to determine how many different ways you can arrange or order a given number of items, you use a factorial.
Learn more about factorials here:
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1/2 : 1
2 : 4
3 : 6
Notice that every ratio consists of a number and double the number.
For 1/2 cup lemon juice, use 1 cup sugar.
The amount of sugar is twice the amount of lemon juice.
The ratio is 1:2
Since you are told the ratio is 1:r, that means r is 2.
The unit rate is 2 cups sugar per cup of lemon juice.
If you would like to know how many centimeters should you cut off, you can calculate this using the following steps:
1 1/2 meters = 3/2 meters = 1.5 meters = 150 centimeters
250 centimeters - 1 1/2 meters = 250 centimeters - 150 centimeters = 100 centimeters = 1 meter
The correct result would be 100 centimeters.
