combination

Examples of combination in the following topics:

• Combinations

  • In smaller cases, it is possible to count the number of combinations.
  • Combinations can refer to the combination of $n$ things taken $k$ at a time with or without repetition.
  • Combination problems involve such scenarios.
  • Each possible combination of $k$ distinct elements of a set $S$ is known as a $k$-combination.
  • If the set has $n$ elements, the number of $k$-combinations is equal to

• Combined Variation

  • Combined variation describes the relationship between three or more variables that vary directly and inversely with one another.
  • Combined variation is used to describe the relationship between three or more variables that vary directly and inversely with one another.
  • Before go deeper into the concept of combined variation, it is important to first understand what direct and inverse variation mean.
  • A practical example of combined variation is the Combined Gas Law, which relates the pressure (p), volume (v), moles (n), and temperature (T) of a sample of gas:
  • Apply the techniques learned with direct and inverse variation to combined variation

• Adding and Subtracting Polynomials

  • Recall the rules for adding and subtracting algebraic expressions, which state that only like terms can be combined.
  • If any term does not have a like term in the other polynomial, it does not need to be combined with any other term.

• Complex Fractions

  • The process of simplifying complex fractions, known as the "combine-divide method," is as follows:
  • Since there are no terms that can be combined or simplified in either the numerator or denominator, we'll skip to Step 3, dividing the numerator by the denominator:
  • Start with Step 1 of the combine-divide method above: combine the terms in the numerator.
  • Let's move on to Step 2: combine the terms in the denominator.

• Negative Numbers

  • The underlying principle is that two debts—negative numbers— can be combined into a single debt of greater magnitude.
  • Here, a credit of 8 is combined with a debt of 3, which yields a total credit of 5.
  • Here, a debt of 2 is combined with a credit of 7.

• Basic Operations

  • In its simplest form, addition combines two quantities into a single quantity, or sum.
  • If you combine both groups together, you now have one group of 5 boxes.
  • Multiplication also combines multiple quantities into a single quantity, called the product.

• Theoretical Probability

  • A combination is an arrangement of unique objects, in which order is not important.
  • For example, the number of possible combinations of $n$ objects arranged in groups of size $r$ can be calculated by:

• Simplifying Exponential Expressions

  • However, they also apply to expressions involving a combination of both integers and variables.
  • Combining the two terms, our original expression simplifies to $a^5 + 8b^6$.

• Adding and Subtracting Algebraic Expressions

  • We can simplify an algebraic expression by combining the like terms.
  • So we could rearrange the following expression before combining like terms: $4a + 6b + 2a +b$

• Linear Inequalities

  • Step 1, combine like terms on each side of the inequality symbol: $-6x+3\leq-4x-9$
  • Step 2, since there is a variable on both sides of the inequality, choose to move the $-4x$, to combine the variables on the left hand side of the inequality, or move the $-6x$ to the right hand side of the inequality.