Question

# How many strings are there of four lowercase letters that

Factors and multiples
How many strings are there of four lowercase letters that have the letter x in them?

2021-08-17
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