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How many ways are there to select exactly four clocks from a store with 10 wall-clocks and 16 stand-clocks?

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How many ways are there to select exactly four clocks from a store with 10 wall-clocks and 16 stand-clocks?

(a) 325

(b) 468

(c) 398

(d) 762

I had been asked this question by my school teacher while I was bunking the class.

The question is from Multiplication Theorem on Probability in portion Discrete Probability of Discrete Mathematics

1 Answer

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Correct option is (a) 325

To elaborate: To choose any clock for the first pick, there are 10+16=26 options. For the second choice, we have 25 clocks left to choose from and so on. Thus, by the rule of product, there are 26 * 25 * 24 * 23 = 650 possible ways to choose exactly four clocks. However, we have counted every clock combination twice. Hence, the correct number of possible ways are 650/2 = 325.

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