how many sequences of 0s and 1s of length 19 are there that begin with a 0, end with a 0, contain no two consecutive 0s, and contain no three consecutive 1s? (2019 amc 10 b)

There are 65, 19-bit sequences of 0s and 1s that start with a 0 and end with a 0 that exist.

Explain the term sequences?

A grouping of numbers in such a specific order is known as a sequence.

On the other perspective, a series is described as the accumulation of a sequence’s constituent parts.

Any subsequent 0 in the sequence must come exactly two or three spots down from the previous one.

We begin at point 1 and finish at position 19 in this instance.

That is, we advance along the line a whole of 18 positions.

In order to achieve 18, we must add all series consecutive 2s and 3s.

There are numerous methods for doing this:

Case 1: There is just one possible arrangement for nine 2s.

Case 2: Two 3s with six 2s – thus ⁸C₂ ways = 28 ways

Case 3: Four 3s with three 2s – thus ⁷C₄ ways = 35 ways

Case 4: Six 3s – Only 1 way to arrange.

Thus, the number of arrangements = 1 + 28 + 35 + 1 = 65 .

Therefore ,the total possible number of the sequencethat cane be made is 65 .

19-bit sequencesof 0s and 1s that start with a 0 and end with a 0 that exist.## Explain the term sequences?

consecutive2s and 3s.arrangementfor nine 2s.sequences,herehttps://brainly.com/question/7882626