How many bit strings of length 5 contain at least two 1s?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Discrete Math:
How many bit strings of length 5 contain at least two 1s?
Expert Solution
Step 1
We first find number of bit strings of length 5 that contain less than two 1s.
(1) When there is no 1s in bit strings of length 5. (contain only zero)
Number of such string =
(2) When there is only one 1s in the bit strings of length 5.
Number of such strings =
Hence we have 6 strings ( from (1) and (2) ) that contain less than two 1s. The rest of the strings contain at least two 1s.
Also
the total number of bit strings of length 5 =
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