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
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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 = C05 = 5!0!(5-0)! = 5!5! = 1            Crn = n!r!(n-r)!

(2) When there is only one 1s in the bit strings of length 5.

Number of such strings = C15 = 5!1!(5-4)! = 5

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  = 25 =32

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