Final answer:
To find the number of bit strings of length 12 that contain exactly three 1s, we can use combinations. The total number of bit strings is 672.
Step-by-step explanation:
To find the number of bit strings of length 12 that contain exactly three 1s, we can use the concept of combinations.
Since we want exactly three 1s and the remaining digits can be 0s, there are 9 positions available for the 1s.
The number of ways to choose 3 positions out of the 9 available is given by the combination formula C(9, 3) = 84.
Each position can be either 1 or 0, so for each combination of positions, there are 2^3 = 8 possible arrangements of 1s and 0s.
Therefore, the total number of bit strings of length 12 containing exactly three 1s is 84 * 8 = 672.