Question

1. Numbers arranged in a specific order factorial 2. An array of numbers 0! 3. A symbol for a sum Sigma 4. A series whose terms are formed by addition series 5. 1 combinations 6. A series whose terms are formed by multiplication geometric series 7. Symbol is ! permutation 8. A set of elements that does not consider order sequence 9. A study of likelihoods Pascal's triangle 10. A sum of numbers in a specific order probability 11. A set of elements in a specific order arithmetic series

Answer 1

The student's question revolves around key mathematical concepts such as factorial, permutation, combination, series, and the binomial theorem, which are all essential in understanding algebra and probability in high school mathematics.

Step-by-step explanation:

The student's question involves various concepts of mathematics, specifically those found in algebra, probability, and sequences. To address the question, it is crucial to understand terms like factorial, permutation, combination, series, arithmetic and geometric sequences, and the binomial theorem. Factorial is a product of all positive integers up to a given number and is represented by an exclamation mark, such as factorial 2, which is written as 2!. Permutation deals with the arrangement of objects in a specific order, while combination represents the selection of items without considering the order. Sequences can be arithmetic, where each term differs from the next by a constant, or geometric, where each term is a fixed multiple of the previous one.

The binomial theorem is a method in algebra for expanding expressions raised to a power, represented as (a + b)^n. The expression expands into a series that involves factorials, terms of a and b, and powers based on the position in the series. Scientific notation, often a part of exponential arithmetic, is a concise way to express large or small numbers, utilizing powers of ten. It is commonly used alongside large numbers or in calculations involving physics and chemistry.