How many binary words of length 8 are there that contain at least six 1's?
This is what I have:
8!/6!2! = 28 words
Is this the correct answer?
2026-03-27 14:59:00.1774623540
AM I doing this right? - How many binary words of length 8 are there that contain at least six 1's?
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You're on the right track, but that only counts those containing exactly 6 ones.
You want to count those containing at least 6 ones; meaning those containing 6, 7, or 8 ones.
Use the same principle and add them together.
$$\frac{8!}{2!6!}+ \frac{8!}{1!7!}+\frac{8!}{0!8!} = 37$$