Consider the eight bit strings of length 3. Let’s find the number of strings that start with 1 or have weight 2 (i.e., contain exactly two 1s).
(a)
List all the 3-bit strings that start with 1.
(b)
List all the 3-bit strings that have weight 2.
(c)
Now list all the 3-bit strings that start with 1 or have weight 2. But be lazy: don’t list them from scratch, use your lists from the two tasks above.
(d)
How many strings are there in your lists?
Strings that start with 1:
Strings of weight 2:
Strings that start with 1 or have weight 2:
Strings that both start with a 1 and have weight 2:
2.
How did you combine your two lists above? Explain how you did it. Then think of another method you could have used and explain how that would be different.
3.
Xiang and Omari are discussing their favorite mathematicians throughout history. Xiang has a list of 7 favorites, while Omari has a list of 5. They discover that they have 3 mathematicians in common. How many mathematicians are on their combined list?
