Practice problem
Counting and Probability: Word Problems
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In English, most sentences follow a specific word order: --. This is a general way of representing the different parts that make up a sentence. The of a sentence is the main focus of the sentence—typically the person that performs some action. The of a sentence is the action happening in the sentence. The of a sentence is whatever is acted on. A sentence can also have other components in any order.
Let’s define a Yoda sentence as a sentence that does not have -- order.
For example, these are valid Yoda Sentences (with other components italicized):
, my young padawan.
Mind what you have learned. .
, my old padawan.
While this is not:
Do or do not, .
Suppose you are given a sentence with components, of which are exactly a , a , and an . Assuming the other components can appear in any order and still be grammatically correct, how many valid Yoda sentences are there using these components?