A bridge is supported by 12 columns. Stress is to be measured in each of the col

Question

A bridge is supported by 12 columns. Stress is to be measured in each of the columns, and the measurements are to be conducted simultaneously in as many columns as technically possible. There are three sensors available for measurements.

a) if all three sensors are the same, in how many ways can they be deployed?

b) if all three sensors are different, how many ways are there to deploy them?

c) if two sensors are the same and the third one is different, in how many ways can they be deployed?

I'm having trouble with part C only, please include reasoning behind the answer achieved.

The correct answer is 660

Explanation / Answer

first one can be deployed in 12 ways and 2nd one in 11 ways and 3rd in 10 ways. so total ways is 12*11*10 if all are different,. Since in this case 2 of the sensors are same. the ways need to be divided by 2! thus answer is 12*11*10/2 =660

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