Question

An old man while dialing a 7 digit telephone number remembers that the first four digits consists of one 1

Answer 1

I think your question is incomplete .

Answer 2

As the question is incomplete, I'm gonna give u an idea to solve this kind of problems.

Let's assume the old man knows all the numbers. He is just confused about the first 4 numbers due to the position of one '1'. That means he is definite about the last 3 numbers of the 7 numbered phone number.

Now, for the first 4 numbers;

i) Here, he puts the '1' in the first place.

1 _ _ _  So for the next position, he'll have 3 choices(because among 4 numbers he already used '1'). He puts anyone in the 2nd spot. Now he'll have 2 choices(because among 4 numbers 2 are already used). Now for the last spot he'll have no choice but putting the remaining number.

Thus, in this manner, number of phone numbers actually can be dialled = 3 X 2 X 1 = 6

ii) _ 1 _ _ So, if he puts the '1' in second position he'll also have 6 numbers to dial.

'1' can be put in 4 places, each place will produce 6 new numbers.

Thus, total numbers possible = 4 X 6 = 24(condition: no number is repeated).