Just complete question D: Problem:

Consider a regular $2\backslash$times n snakes and ladders board. We are interested in placing two snakes, but each must be in a separate row $($the rule that head must be greater than tail is still required$).$ An example is shown below:

$($a$)$ Use the product rule to figure out the number of ways we can place the two snakes. Explain your reasoning. The answer must be for a general n$.$

$($b$)$ The board has n columns. If a head or a tail of any snake falls in a given column, we say that the column is involved. In the example above, four columns are involved. Give an example of placing the two snakes where two columns are involved, and another one where three columns are involved.

$($c$)$ Find the number of ways you can place the two snakes if:

Two columns are involved

Three columns are involved

Four columns are involved

Hint: There are multiple ways of doing this, but mostly the product rule should be helpful.

$($d$)$ What does the addition rule guarantee about your answer for $($a$)$ and the three answers in $($c$)?$ Verify.Example $n=8$