Alex wishes to plant three different fruit trees in his front yard. He has five different types of fruit trees he can choose from: cherry, plum, apple, peach, and pear. How many different combinations of fruit trees are possible?
Solving Combinations: the Listing Method:
To solve the example problem, label the five possible elements (in this case trees) A, B, C, D and E. Now begin listing out the possibilities (keeping in mind that arrangement doesn't matter). One trick is to list out the possibilities in alphabetical order starting with ABC, and to work your way through the possibilities: ABC, ABD, ABE, ACD and so on.
Solving Combinations: the Formula Method:
If you prefer not to use the Listing Method, the formula for solving for the number of combinations is as follows:
n = the number in the larger group
k = the number you're combining (# in the smaller group)
Pick whichever method works for you.
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Video Lessons and 10 Fully Explained Grand Tests
Large number of solved practice MCQ with explanations. Video Lessons and 10 Fully explained Grand/Full Tests.