Combinations

The first instance of  is under the Probability and statistics Math Mission. This exercise practices calculating combinations.

Types of Problems
There is one type of problem in this exercise:


 * 1) Perform combination: This problem describes a situation where a collection of objects is selected from a larger group and the order does not matter. The student is supposed to find how many combinations are possible and place that answer in the appropriate area.Comb1.png

Strategies
This exercise is easy to get accuracy and speed badges because there is only one type of problem and the formula is straightforward. Speed badges are especially easy if you know how to use a calculator to calculate combinations.


 * 1) The formula for r objects being chosen from a collection of n (order does not matter) is $$n!/((n-r)!r!)$$.
 * 2) Some useful factorials to know are $$5!=120, 4!=24, 3!=6, 2!=2, 1!=1, 0!=1$$.
 * 3) If you have n objects and you need to select r, you can write a fraction with r slots in the numerator and r slots in the denominator. Write decreasing consecutive numbers starting from n in the numerator, and decreasing consecutive numbers starting from r in the denominator. Simplify, and that is the answer.
 * 4) The solution to a combination is always an integer. If you are not getting an integer, you have calculated incorrectly.