(a) Suppose a security code can be any string of five or fewer digits in length.
ID: 3871512 • Letter: #
Question
(a) Suppose a security code can be any string of five or fewer digits in length. How many security codes are there?
(b) A typical image on the internet is of size 640 × 480. (How many pixels does it contain?) Let's focus on images of a smaller size, say 10 × 10 (about the size of an alphabetic character on the screen). And let's assume there are just two possible colors for each pixel, black and white. Write a mathematical expression for the number of different possible black-and-white 10 × 10 images?
Explanation / Answer
a) As only digits are allowed i.e. from 0 to 9, and it can be of length from 1 to 5,
Number of security code of length 1 is 10
Number of security code of length 2 is 10*10
Number of security code of length 3 is 10*10*10
Number of security code of length 4 is 10*10*10*10
Number of security code of length 5 is 10*10*10*10*10
Total number of security code (Adding all) = 111110
b) Number of pixels are 640*480 = 307200 pixels
As every pixel can be black or white, and size of image is 10*10, so there are 100 pixels, and every can be either black or white, so we have two choices for every pixel.
Total number of possible images = 2*2*2*...100 times
=2^100
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