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The number of digits in a mobile phone number decide the maximum mobile phones we can have without dialing the country code, ie. 91 (for India). To understand this we need to go back to school.Remember permutations & combinations.
Suppose I had a pair of jeans (J1-2) and four tee-shirts (T1-4). The possible combinations are J1T1, J1T2, J1T3, J1T4, J2T1, J2T2, J2T3, and J2T4, ie. 8 combinations {2 (no. of jeans) X 4 (no. of tee-shirts)}.

The same logic is used when computing the digits in a mobile phone number. Now suppose if we had a 6-digit cell number, the maximum number of unique cell numbers possible would have been (10 x 10 x 10 x 10 x 10 x 10), ie, a maximum of 1,000,000 subscribers. We have already crossed the 100-million mark in India. So obviously we could not have had a 6-digit cell phone number. Not even a 7-digit because that would've resulted in a capacity of 10 million, not even 8-digit (100 million subscribers), and not even a 9-digit (ie. 1000 million or 100 crores, since our population is close to 125 crores and growing).

A 10-digit cell number offers us a capacity to have 10 million (1000 crore) subscribers, which is far more than what our country can even achieve. We are v.v.v.unlikely to have a population or a subscriber base of 1000 crore but there is a remote likelihood of us having 100 crore subscribers. Hence, a 10-digit mobile number.

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Q: Why mobile numbers are 10 digit only?
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What is the number of 5 digit telephone numbers having atleast one of their digits repeated?

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