How many 6 digit numbers are formed with the digits 0,1,2,3,4,5,6,7 ?
How many 6 digit numbers are formed with the digits 0,1,2,3,4,5,6,7 ?
Solution and Explanation
To determine how many six-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, and 7, we need to consider the number of choices for each digit position.
For the first digit position (leftmost), we have 7 choices (excluding 0 since a six-digit number cannot start with 0).
For the remaining five digit positions (from left to right), we have 8 choices (including 0) since all digits are available.
Therefore, the total number of six-digit numbers that can be formed is obtained by multiplying the number of choices for each digit position:
Total number of six-digit numbers = 7 * 8 * 8 * 8 * 8 * 8 = 7 * 8^5 = 7 * 32768 = 229,376
Hence, there are 229,376 six-digit numbers that can be formed using the digits 0, 1, 2, 3, 4, 5, 6, and 7.
Top Questions on permutations and combinations
- In an examination of Mathematics paper, there are 20 questions of equal marks and the question paper is divided into three sections : A, B and C . A student is required to attempt total 15 questions taking at least 4 questions from each section. If section A has 8 questions, section B has 6 questions and section C has 6 questions, then the total number of ways a student can select 15 questions is _______ .
- JEE Main - 2024
- Mathematics
- permutations and combinations
- A local restaurant has 16 vegetarian items and 9 non-vegetarian items in their menu. Some items contain gluten, while the rest are gluten-free.
One evening, Rohit and his friends went to the restaurant. They planned to choose two different vegetarian items and three different non-vegetarian items from the entire menu. Later, Bela and her friends also went to the same restaurant: they planned to choose two different vegetarian items and one non-vegetarian item only from the gluten-free options. The number of item combinations that Rohit and his friends could choose from, given their plan, was 12 times the number of item combinations that Bela and her friends could choose from, given their plan.
How many menu items contain gluten?- XAT - 2024
- Quantitative Ability and Data Interpretation
- permutations and combinations
- The lines $L_1, L_2, \ldots, L_{20}$ are distinct. For $n = 1, 2, 3, \ldots, 10$, all the lines $L_{2n-1}$ are parallel to each other, and all the lines $L_{2n}$ pass through a given point $P$. The maximum number of points of intersection of pairs of lines from the set $\{L_1, L_2, \ldots, L_{20}\}$ is equal to:
- JEE Main - 2024
- Mathematics
- permutations and combinations
- If all the words with or without meaning made using all the letters of the word "NAGPUR" are arranged as in a dictionary, then the word at 315th position in this arrangement is
- JEE Main - 2024
- Mathematics
- permutations and combinations
- Let the set $S = \{2, 4, 8, 16, ..., 512\}$ be partitioned into 3 sets $A, B, C$ with equal number of elements such that $A \cup B \cup C = S$ and $A \cap B = B \cap C = A \cap C = \phi$. The maximum number of such possible partitions of $S$ is equal to:
- JEE Main - 2024
- Mathematics
- permutations and combinations
Questions Asked in AP EAMCET exam
Six coins tossed simultaneously then find the probability of getting at least 4 heads.
- AP EAMCET - 2023
- Probability
- In the chessboard if the rectangle form is 1296, find the total number of squares formed.
- AP EAMCET - 2023
- Coordinate Geometry
Find the products formed if chlorine reacts with the cold and dilute sodium hydroxide solution.
- AP EAMCET - 2023
- Chemical Reactions
- Find the coefficient of \(\frac{y^3}{x^8}\) in \((x+y)^{-5}\) ?
- AP EAMCET - 2023
- Binomial theorem
- Which compound is gem-dihalide?
- AP EAMCET - 2023
- Organic Chemistry- Some Basic Principles and Techniques
Concepts Used:
Permutations and Combinations
Permutation:
Permutation is the method or the act of arranging members of a set into an order or a sequence.
- In the process of rearranging the numbers, subsets of sets are created to determine all possible arrangement sequences of a single data point.
- A permutation is used in many events of daily life. It is used for a list of data where the data order matters.
Combination:
Combination is the method of forming subsets by selecting data from a larger set in a way that the selection order does not matter.
- Combination refers to the combination of about n things taken k at a time without any repetition.
- The combination is used for a group of data where the order of data does not matter.