A binary string is a sequence of zeros and ones such as 00101101. a) How many di

Question

A binary string is a sequence of zeros and ones such as 00101101. a) How many different binary strings of length 8 contain at most three 1's? b) How many different binary strings of length 8 contain at least two 1's? c) In how many ways can you rearrange the letters in AABBBCCCC? An alphanumeric string is a sequence of numbers and letters such as 1BC3FGGG5. a) How many alphanumeric strings of length 15 can be made using 10 capital letters and 5 numbers if you are not allowed to have two numbers next to each other? b) How many alphanumeric strings of length 15 can be made using 10 capital letters and 5 numbers if you are not allowed to have two numbers next to each other and the letters all have to be distinct?

Explanation / Answer

Dear Student Thank you for using Chegg !! Given a binary string of length 8 characters a) At most 3 1's Number of strings with zero 1 = 1 (All zeroes) Number of strings with one 1 = 8! / 7! = 8 Number of strings with two 1 = 8! / 2! * 6! = 28 Number of strings with three 1 = 8! / 3! * 5! = 56 Solution = 1+8+28+56 = 93 b)At least two 1's Number of strings with zero 1 = 1 (All zeroes) Number of strings with one 1 = 8! / 7! = 8 Total Number of binary strings possible = 2^8 Number of strings with atleast two 1's = 2^8 - 1 - 8 247 Solution c) Number of ways to rearrange AABBBCCCC = 9 ! / 2!*3!*4* = 1260 Solution

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