a. Your sweet new bicycle has 3 front sprockets and 7 rear sprockets. Each disti

Question

a. Your sweet new bicycle has 3 front sprockets and 7 rear sprockets. Each distinct combination of a front sprocket with a rear sprocket constitutes a different gear on a bicycle. How many gears does your bicycle have?

b. Is it correct to say that a particular speed requires a particular front sprocket or a particular rear sprocket, or is it correct to say that a particular speed requires a particular front sprocket and a particular rear sprocket?

Your sweet new bicycle has 3 front sprockets and 7 rear sprockets. Each distinct combination of a front sprocket with a rear sprocket constitutes a different gear on a bicycle. How many gears does your bicycle have? Is it correct to say that a particular speed requires a particular front sprocket or a particular rear sprocket, or is it correct to say that a particular speed requires a particular front sprocket and a particular rear sprocket? Choose... and or

Explanation / Answer

(A)

As each combination of front sprocket with a rear sprocket constitute a different gear, we need to find the different combinations of a front sprocket with a rear sprocket. As we had 3 front sprocket, one can be selected in 3C1 = 3 ways. One rear sprocket can be selected from 7 sprockets in 7C1 = 7 ways.

So total number of gears = 3 * 7 = 21.

(b) And .

A particular speed requires a bicycle to move constatly in a particular gear. In this case a particular combination of a front sprocket and a rear sprocket together constitute gear. So, it is correct to say that a particular speed requires a particular front sprockat and a particular rear sprocket.

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