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The code for a safe is of the form PPPQQQQ where P is any number from 0 to 9 and Q represents the letters of the alphabet. How many codes are possible for each of the following cases? Note that the digits and letters of the alphabet can be repeated.

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The code for a safe is of the form PPPQQQQ where P is any number from 0 to 9 and Q represents the letters of the alphabet. How many codes are possible for each of the following cases? Note that the digits and letters of the alphabet can be repeated.

(a) 874261140

(b) 537856330

(c) 549872700

(d) 456976000

The question was posed to me by my college professor while I was bunking the class.

My enquiry is from Fundamental Principle of Counting in portion Counting of Discrete Mathematics

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The correct answer is (d) 456976000

To elaborate: 10^3 × 2^64 = 456976000 possible codes are formed for the safe with the alphanumeric digits.

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