How many bit strings of length 10 have more 0s than 1s?

Tyra

Tyra

Answered question

2021-10-28

How many bit strings of length 10 have more 0s than 1s?

Answer & Explanation

Velsenw

Velsenw

Skilled2021-10-29Added 91 answers

When less than five of the ten bits are ones, there are more 0s than 1s.
n=10 
r<5 
Consider the following when defining a combination:
C(10,4)=10!4!(104)!=10!4!6!=210 
C(10,3)=10!3!(103)!=10!3!7!=120 
C(10,2)=10!2!(102)!=10!2!8!=45 
C(10,1)=10!1!(101)!=10!1!9!=10 
C(10,0)=10!0!(100)!=10!0!10!=1 
For each value of r, multiply the total number of bit strings:
210+120+45+10+1=386

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