(2) More inclusion-exclusion counting: How many bit strings of length 15 have bits 1, 2, and...

(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 means some special care will be needed to get the count correct.

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