Solution:

There are 26 possible letters in the alphabet

Strings of lentgth 4 We need to use the product rule, because the first event is picking the first bit, the second event is picking the second bit, ... , the 4th event is picking the 4th bit.

\(\displaystyle{26}\cdot{26}\cdot{26}\cdot{26}={26}^{{4}}={456},{976}\)

Strings of length 4 without an x. We need to use the product rule, because the first event is picking the first bit, the second event is picking the second bit, the 4th event is picking the 4th bit.

\(\displaystyle{25}\cdot{25}\cdot{25}\cdot{25}={25}^{{4}}={390},{625}\)

Strings of length 4 with at least one x. Strings of length 4 with at least one x are strings of length 4 that are not strings of length 4 without an x

\(\displaystyle{456},{976}-{390},{625}={66},{351}\)

Result:

66,351 strings

There are 26 possible letters in the alphabet

Strings of lentgth 4 We need to use the product rule, because the first event is picking the first bit, the second event is picking the second bit, ... , the 4th event is picking the 4th bit.

\(\displaystyle{26}\cdot{26}\cdot{26}\cdot{26}={26}^{{4}}={456},{976}\)

Strings of length 4 without an x. We need to use the product rule, because the first event is picking the first bit, the second event is picking the second bit, the 4th event is picking the 4th bit.

\(\displaystyle{25}\cdot{25}\cdot{25}\cdot{25}={25}^{{4}}={390},{625}\)

Strings of length 4 with at least one x. Strings of length 4 with at least one x are strings of length 4 that are not strings of length 4 without an x

\(\displaystyle{456},{976}-{390},{625}={66},{351}\)

Result:

66,351 strings