### How many strings are there of four lowercase letters that have the letter (x) in them?

The main purpose of this question is to find the number of strings of four specific lowercase letters that have the letter $x$ in them. Bit strings depict subsets of sets, in which a $1$ indicates that the associated component of a set is a part of the subset and a $0$ indicates that it […]

### How many bit strings of length seven either begin with two 0s or end with three 1s?

The purpose of this question is to find the number of bit-strings of length $7$ beginning with two $0$s and ending with three $1$s. The sequence of binary digits is usually called a bit-string. The number of bits signifies the value length in the sequence. A bit-string having no length is regarded as a null […]

### Thirteen people on a softball team show up for a game. How many ways are there to assign the 10 positions by selecting players from the 13 people who show up?

This question aims to find the possible number of ways $10$ positions can be assigned to the players out of a team of $13$. A mathematical method that is used to work out the number of potential groupings in a set when the order of grouping is required. An ordinary mathematical problem involves selecting only […]

### Prove or disprove that if a and b are rational numbers, then a^b is also rational.

The main objective of this question is to prove or disprove that $a^b$ is a rational number provided that $a$ and $b$ are rational numbers. In arithmetic, a rational number is a number that can be expressed as the ratio $dfrac{a}{b}$ of two integers such that $b neq 0$. Apart from fractions, the set of rational numbers […]

### A discounted amusement park ticket costs \$12.95 less than the original price p. Write and solve an equation to find the original price.

This article aims to find the original price of the ticket, given the discounted price and discount. The article uses the definitions of the original price, discount, and discounted price. To calculate original price of a discounted or sale item, you need to know the sale price and discount percentage. The calculations involve a simple formula that divides […]