Question

How many bit strings of length 10 have... (a) Exactly four 1s in a row? (b) at least eight 0s in a row?

Answer 1

(a) Exactly four 1s in a row?

n=10

r=4

Evaluate the defination of a combinatio:

C(10,4)=10! / 4!(10−4)!=210

(b) at least eight 0s in a row?

n=10

r>=8

C(10,8)=10! / 8!(10−8)!=45

C(10,9)=10! / 9!(10−9)!=10

C(10,10)=10! / 10!(10−10)!=1

Add the number of bit strings for each value of r:

45+10+1=56