Question

How many different numbers which are smaller than

2.10^8

can be formed using the digits 1 and 2 only?​

Answer 1

Answer:

What are the number of natural numbers which are smaller than 2*10^8 and which contain only the digits 1 and 2?

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Question: What are the number of natural numbers which are smaller than 2*10^8 and which contain only the digits 1 and 2?

Solution:

Break the question into many parts by number of digits:

Single digit numbers = C1=2=1, 2

2-digit numbers: C2=2∗2=4 [ ∵ First digit in 2 ways, second digit in 2 ways ]

3-digit numbers: C3=2∗2∗2=8

4-digit numbers: C3=2∗2∗2∗2=16

….

8 digit numbers: C8=28=256

9 digit numbers: C9=1∗28=256 [ ∵ the first digit can only be 1 so that the number will be less than 2∗108 ]

Total numbers that can be made = ∑i=19Ci

=2+4+8+16+...+256+256=766