Answer to Question #252638 in Discrete Mathematics for nurul

Question

(a)How many bit strings of length 8 contain at least 6 ones?

(b)How many bit strings of length 8 contain at least 3 ones and 3 zeros?

Answer 1

(a) The amount of strings of lenght 8 that contain at least 6 ones is the sum of the amounts of the strings that contains exactly 6, 7, 8 ones

The amount of the strings of lenght 8 that contain at least 6 ones is ${8 \choose 6} +{8 \choose 7}+{8 \choose 8}=28+8+1=37$ strings

(b) The amount of string that contains at least 3 ones and 3 zeros is the sum of the amounts of the strings that contain exactly 3, 4, 5 ones (other places will be automatically taken by zeros)

${8 \choose 3}+{8 \choose 4}+{8 \choose 5} = 56 +70+ 56= 182$ strings