The number of natural numbers which are less than 2 . 10 8 and which can be written by means of the digit 1 and 2 is -
Text Solution
Verified by ExpertsD
The required numbers are
1, 2, 11, 12, 21, 22, …. , 122222222
Let us calculate how many numbers are these.
There are 2 one-digit such numbers. There are 22 two-digit such numbers and so on.
There are 2 8 eight-digit such numbers. All the digit numbers beginning with 1 and written by means of 1 and 2 are smaller than 2. 10 8 . Thus, there are 2 8 such nine-digit numbers.
Hence the required number of numbers is
2 + 2 2 + 2 3 + …. + 2 8 + 2 8 = 
+ 2
8 = 2 9 – 2 + 2 8 = 766.
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems