Why do we have a 10-digit mobile number? Why not 6/7/8/9-digit?

Why do we have 10-digit mobile numbers? This is probably something most of us do not really think about. But it has a very sound logic to it. And, I realised the same today while reading a book "Innumeracy" by John Allen Paulos.

The logic: 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 or for that any numbers such as those for vehicles, land-line telephone numbers, etc. 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 crore, since our population is close to 125 crore and growing).

A 10-digit cell number offers us a capacity to have 10 billion (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 phone number.