
How many numbers can be formed from the digits 1,2,3,4 when the repetition is not allowed
A. $^{4}{{\text{P}}_{4}}$
B. ${ }^{4} \mathrm{P}_{3}$
C. $^{4}{{\text{P}}_{1}}{{+}^{4}}{{\text{P}}_{2}}{{+}^{4}}{{\text{P}}_{3}}$
D. ${ }^{4} \mathrm{P}_{1}+{ }^{4} \mathrm{P}_{2}+{ }^{4} \mathrm{P}_{3}+{ }^{4} \mathrm{P}_{4}$
Answer
164.7k+ views
Hint: Basically A permutation is a grouping of items in a specific direction or sequence. One should consider both the selection and the arrangement while dealing with permutation. In permutations, ordering is crucially important. The permutation is seen as an ordered combination, in other words.
Complete step by step solution:
A permutation is a configuration of objects in a particular order. Here, the components of sets are arranged in a linear or sequential order. For instance, the set $A=1,6$ has a permutation of 2, which is 1,6,1. There is no other way to organize the components of set A, as you can see.
While the order of the ingredients isn't important in combination, it should be followed while performing permutations. Additionally, see Permutation and Combination.
Here in the given question,
There are 4 numbers . Then without repetition it can form numbers $^{4}{P}_{4}$ times
Consider $n=4$ and $r=4$ in order to analyze the aforementioned. and apply the permutations formula $p(n, r)={ }^{n}P_{r}=\dfrac{n !}{(n-r) !}$to determine how many combinations may be created by selecting 4 items from the total, which is likewise 4. All conceivable options will be covered in the response you receive.
$P(n, r)={ }^{n}P_{r}=\dfrac{n !}{(n-r) !}$
${ }^{4}P_{4}=\dfrac{4 \times 3 \times 2 \times 1}{1}$
${ }^{4}P_{4}=24$
Option ‘A’ is correct
Note: The number of maximum digit numbers formed using the digits 1, 2, 3, 4 when repetition is not allowed is equivalent to the number of 4 Letter permutations of 4 distinct letters.
Complete step by step solution:
A permutation is a configuration of objects in a particular order. Here, the components of sets are arranged in a linear or sequential order. For instance, the set $A=1,6$ has a permutation of 2, which is 1,6,1. There is no other way to organize the components of set A, as you can see.
While the order of the ingredients isn't important in combination, it should be followed while performing permutations. Additionally, see Permutation and Combination.
Here in the given question,
There are 4 numbers . Then without repetition it can form numbers $^{4}{P}_{4}$ times
Consider $n=4$ and $r=4$ in order to analyze the aforementioned. and apply the permutations formula $p(n, r)={ }^{n}P_{r}=\dfrac{n !}{(n-r) !}$to determine how many combinations may be created by selecting 4 items from the total, which is likewise 4. All conceivable options will be covered in the response you receive.
$P(n, r)={ }^{n}P_{r}=\dfrac{n !}{(n-r) !}$
${ }^{4}P_{4}=\dfrac{4 \times 3 \times 2 \times 1}{1}$
${ }^{4}P_{4}=24$
Option ‘A’ is correct
Note: The number of maximum digit numbers formed using the digits 1, 2, 3, 4 when repetition is not allowed is equivalent to the number of 4 Letter permutations of 4 distinct letters.
Recently Updated Pages
Geometry of Complex Numbers – Topics, Reception, Audience and Related Readings

JEE Main 2021 July 25 Shift 1 Question Paper with Answer Key

JEE Main 2021 July 22 Shift 2 Question Paper with Answer Key

JEE Main 2025 Session 2: Exam Date, Admit Card, Syllabus, & More

JEE Atomic Structure and Chemical Bonding important Concepts and Tips

JEE Amino Acids and Peptides Important Concepts and Tips for Exam Preparation

Trending doubts
Atomic Structure - Electrons, Protons, Neutrons and Atomic Models

Learn About Angle Of Deviation In Prism: JEE Main Physics 2025

JEE Main Chemistry Question Paper with Answer Keys and Solutions

JoSAA JEE Main & Advanced 2025 Counselling: Registration Dates, Documents, Fees, Seat Allotment & Cut‑offs

NIT Raipur Cut-off of Previous Years and Expected for 2025

JEE Main Eligibility Criteria 2025

Other Pages
NCERT Solutions for Class 11 Maths Chapter 6 Permutations and Combinations

JEE Advanced 2025 Notes

Total MBBS Seats in India 2025: Government College Seat Matrix

NEET Total Marks 2025: Important Information and Key Updates

Neet Cut Off 2025 for MBBS in Tamilnadu: AIQ & State Quota Analysis

Karnataka NEET Cut off 2025 - Category Wise Cut Off Marks
