Answered: "How many bit strings of length 10 have..."

cistG

Answered question

2021-10-25

How many bit strings of length 10 have at least seven 1s?

diskusje5

Skilled2021-10-26Added 82 answers

n=10

r \geq 7

Evaluate the definition of a combination:

C (10, 7) = \frac{10!}{7! (10 - 7)!} = \frac{10!}{7! 3!} = 120

C (10, 8) = \frac{10!}{8! (10 - 8)!} = \frac{10!}{8! 2!} = 45

C (10, 9) = \frac{10!}{9! (10 - 9)!} = \frac{10!}{9! 1!} = 10

C (10, 10) = \frac{10!}{10! (10 - 10)!} = \frac{10!}{10! 0!} = 1

Add the number of bit strings for each value of r:
120+45+10+1=176

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?