Craftsman sells 10digit keypads that are installed on homes

Craftsman sells 10-digit keypads that are installed on homes to open the garage door. The consumer chooses a 5-number code when programming the keypad. The total number of codes that the consumer can choose from is ________.

252

30,240

57,128

100,000

Solution

As order of the digits does not matter, we use combinations.

hence, there are

10C5 = 10!/[(10-5)!5!] = 252 [ANSWER, A]

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If in case this is a digital keypad, (not the usual manual keypad), then order matters. Hence, there are 10P5 = 30240 ways. [alternative answer]