![]() Algebraic Identity means that the left-hand side of the equation is identical to the right-hand side of the equation, and for all values of the variables. In algebra formulas, an identity is an equation that is always true regardless of the values assigned to the variables. Here, we shall look into the list of all algebraic formulas used across the different math topics. Topics like logarithms, indices, exponents, progressions, permutations, and combinations have their own set of algebraic formulas. The algebraic expression formulas are used to simplify the algebraic expressions.īased on the complexity of the math topics, the algebraic formulas have also been transformed. The algebra formulas are helpful to perform complex calculations in the least time and with fewer steps. Topics like equations, quadratic equations, polynomials, coordinate geometry, calculus, trigonometry, and probability, extensively depend on algebra formulas for understanding and for solving complex problems. Therefore the probability of winning the lottery is 1/13983816 = 0.000 000 071 5 (3sf), which is about a 1 in 14 million chance.Algebra Formulas form the foundation of numerous topics of mathematics. The number of ways of choosing 6 numbers from 49 is 49C 6 = 13 983 816. What is the probability of winning the National Lottery? You win if the 6 balls you pick match the six balls selected by the machine. In the National Lottery, 6 numbers are chosen from 49. The above facts can be used to help solve problems in probability. There are therefore 720 different ways of picking the top three goals. Since the order is important, it is the permutation formula which we use. In the Match of the Day’s goal of the month competition, you had to pick the top 3 goals out of 10. The number of ordered arrangements of r objects taken from n unlike objects is: How many different ways are there of selecting the three balls? There are 10 balls in a bag numbered from 1 to 10. The number of ways of selecting r objects from n unlike objects is: Therefore, the total number of ways is ½ (10-1)! = 181 440 How many different ways can they be seated?Īnti-clockwise and clockwise arrangements are the same. When clockwise and anti-clockwise arrangements are the same, the number of ways is ½ (n – 1)! The number of ways of arranging n unlike objects in a ring when clockwise and anticlockwise arrangements are different is (n – 1)! There are 3 S’s, 2 I’s and 3 T’s in this word, therefore, the number of ways of arranging the letters are: In how many ways can the letters in the word: STATISTICS be arranged? The number of ways of arranging n objects, of which p of one type are alike, q of a second type are alike, r of a third type are alike, etc is: The total number of possible arrangements is therefore 4 × 3 × 2 × 1 = 4! ![]() The third space can be filled by any of the 2 remaining letters and the final space must be filled by the one remaining letter. The second space can be filled by any of the remaining 3 letters. ![]() The first space can be filled by any one of the four letters. This is because there are four spaces to be filled: _, _, _, _ How many different ways can the letters P, Q, R, S be arranged? The number of ways of arranging n unlike objects in a line is n! (pronounced ‘n factorial’). This section covers permutations and combinations. ![]()
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