(2) More inclusion-exclusion counting: How many bit strings of
length 15 have bits 1, 2, and 3 equal to 101, or have bits 12, 13,
14, and 15 equal to 1001 or have bits 3, 4, 5, and 6 equal to 1010?
(Number bits from left to right. In other words, bit #1 is the left
most bit and bit #15 is the right most bit.) Hint: The fact that
the third bit appears in two of the required patterns...