Discrete Structures II

Counting

Can anyone solve number $(9\mathrm{.}125)$please

EXERCISES

For two strings $x$ and $y,$ let's call a shuffle of $x$ and $y$ any interleaving of the letters of the two strings $($that maintains the order

of the letters within each string, but may repeatedly alternate between blocks of x letters and blocks of y letters$).$ For example, the

words ALE and LID can be shuffled into

or

A L

L

I

D

E

or

A

L

L

I

D

E

or

L

I

D

A

L

E

How many different strings can be produced as shuffles of the following pairs of words?

$9\mathrm{.}124$ BACK and FORTH

$9\mathrm{.}125$ DAY and NIGHT