You can make three independent choices, one for each of the three letters. For each choice you have 26 options (the letters in the alphabet). So the total number of combinations is Show $$ 26 \cdot 26 \cdot 26 = 26^3 = 17576. $$ If you want the letters to be unique, the calculation changes slightly. You still have 26 options for the first choice, but for the second choice there are now only 25 options available (all letters except the one you already chose), and for the third choice there are 24 options available (all letters except the two you already chose). So this gives you: $$ 26 \cdot 25 \cdot 24 = 15600. $$ 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. How many different 3 letter combinations can be made from Alphabet?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:
How many ways can 3 letters be arranged?Therefore, the number of ways in which the 3 letters can be arranged, taken all a time, is 3! = 3*2*1 = 6 ways.
How many 3 letter combinations of the alphabet are there?Total number of ways of arranging the letters = 120 x 6 = 720.
How many 3 letter and 3 number combinations are there?Each of the three letter combinations can be combined with any of the three number combinations so the total is 17,576 x 1000 = 17,576,000 different combinations possible.
How many 3 letter combinations are there no repeats?We get that there are 15,600 possible 3-letter passwords, with no letters repeating, that can be made with the letters a through z.
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