As the name implies, a number system is a mathematical system that is used to represent numerals using various symbols and variables. Under the number system, numbers that can be plotted on a number line, commonly known as real numbers, are represented by a set of values or quantities. Based on their various features, distinct sorts of numbers are classified into different sets or groups. For example, rational numbers are any integers that can be represented in the form p/q, where q is a non-zero integer. Decimal, binary, octal, and hexadecimal are examples of different sorts of systems. CombinationsIt is defined as the process of choosing one, two, or a few elements from a given sequence, regardless of the order in which they appear. If you choose two components from a series that only has two elements to begin with, the order of those elements won’t matter. Combination Formula When r items are chosen from n elements in a sequence, the number of combinations is
For example, let n = 7 and r = 3, then number of ways to select 3 elements out of 7 = 7C3 = 7!/3!(7 – 3)! = 35. Solution:
Similar ProblemsProblem 1. Given a piggy bank containing 20 coins, determine the number of permutations of nickels, dimes, and quarters it holds. Solution:
Problem 2. Tell me how many different methods there are to allocate 7 students to a college trip if we only have one triple room and two double rooms. Solution:
Problem 3. Determine the number of ways a five-person committee may be established from a group of seven men and six women, with at least three men on the committee. Solution:
Problem 4. Find the number of ways the letters in the word ‘LEADING’ can be arranged so that the vowels always appear together. Solution:
Problem 5. Find the number of words with four consonants and three vowels that may be made from eight consonants and five vowels. Solution:
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This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level. How many combinations can be using 3 alphabet letters (from A to Z)? Note that string doesn't have to be unique, it can be eg. RPP or AZZ
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