NCERT Solutions for Class 11 Maths Chapter 7 Permutations and Combinations
FAQs on NCERT Solutions for Class 11 Maths Chapter 7: Permutations and Combinations - Exercise 7.3
1. How many 4-digit numbers are there with no digit repeated?
To find the four-digit number (digits does not repeat)
Now we will have 4 places where 4 digits are to be put.
So, in thousand’s position = There are 9 ways as 0 will not be at thousand’s position = 9 ways
In hundredth’s position = There are 9 digits which are to be filled as 1 digit is already taken = 9 ways
In ten’s position = There are now 8 digits that are to be filled as 2 digits are previously taken = 8 ways
At unit’s place = There are 7 digits that can be filled = 7 ways
Total Number of methods to fill the four places = 9 × 9 × 8 × 7 = 4536 ways.
So a total of 4536 four-digit figures can be there with no numbers repeated.
2. What are permutations and combinations?
In mathematics, permutation relates to the act of organizing all the members of a set into some succession or order, or if the set is already arranged, rearranging its components, a process called permuting. Permutations happen, in more or less noticeable ways, in almost all areas of math. They usually arise when various orderings on specific finite sets are recognised.
The combination is a way of choosing items from a group, such that (unlike permutations) the order of preference does not matter. In smaller events, it is possible to figure the number of combinations. Combination introduces the combination of n items taken k at a time without recurrence. To refer to combinations in which recurrence is allowed, the terms k-selection or k-combination with the return are often used.
3. What is the difference between permutations and combinations?
A permutation is used for the list of data (where the order of the data matters) and the combination is used for a collection of data (where the order of data doesn’t matter).
Permutations:
Arranging people, digits, numbers, alphabets, letters, and colours.
Picking a team captain, player or pitcher, and shortstop from a collection.
Picking two favourite colours, in order, from a colour brochure.
Picking first, second and third place winners.
Combinations:
Selection of menu, food, clothes, subjects, team.
Picking three team members from a group.
Picking two colours from a colour brochure.
Picking three winners.
4. How do NCERT answers of Vedantu help me in scoring higher marks?
Our innovative gaining knowledge of methodology in conjunction with the smart and easy study strategies will make your studying methods extra fun, interesting, interactive and in a nicely deliberate way. Our NCERT Solutions for Class eleven Maths have been carefully designed that will help you increase your information base which will, in the end, improve your retention rate.
All the essential and necessary concepts have been included through us in an effort to make your studying much less complicated for examination preparation. They have been crafted from the exam point of view. Our solutions are framed by our experts and they have included each and every part of the concept additionally the exercise questions that are covered at the end of the chapter.
5. What do you understand by factorial notation mentioned in Chapter 7 of Class 11 Maths?
Factorial notation (n!) is the number that you will get after multiplying the first n natural numbers. The product that you will get multiplying 1 x 2 x 3 x 4 x 5..(n - 1)n is known as n! Or factorial notation. For example, 4! will be calculated as 1x2x3x4 = 24. Likewise if you have to calculate 5! - 2!, then you first calculate 5! = 1x2x3x4x5 = 120, then you calculate 2! = 1 x 2 = 2. Now, you subtract 120-2 = 118.
6. Is 3! + 4! = 7!? Determine using the concept used in Chapter 7 of Class 11 Maths.
Let’s have a look at the answer step wise. 3! = 1 x 2 x 3, which is equal to 6; 4! = 1 x 2 x 3 x 4 = 24; 7! = 1 x 2 x 3 x 4 x 5 x 6 x 7, which is equal to 5040. 3! + 4! = 6 + 24 = 30. We can clearly see that 3! + 4! is 30, while 7! is 5040. Therefore, we can establish here that 3! + 4! is not equal to 7!.
7. Which is the best NCERT Solution for Exercise 7.3 of Chapter 7 of Class 11 Maths?
The NCERT Solutions for Exercise 7.3 of Chapter 7 of Class 11 Maths, that you find at Vedantu is the best NCERT Solution manual that you can lay your hands on for solving all the questions based on the respective topic. This solution manual provides answers to all questions from the exercise. Students who solve this exercise from Vedantu’s NCERT Solutions will find the exercise so easy and will be able to finish it in no time. The PDF’s of the Solutions or any study material provided by Vedantu can be downloaded absolutely free of cost.
8. How many 3-digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6, if the digits can be repeated? Solve by the method used in Chapter 7 of Class 11 Maths.
To get 3-digit even numbers, we know that in the one place of these digits, there should be even numbers, which can be filled in 3 ways (either 2, 4 or 6). The tens and hundreds place can be filled in 6 ways each as the digits can be repeated. So going by the multiplication rule, the number of 3-digit even numbers formed from digits 1, 2, 3, 4, 5, and 6 would be 3 x 6 x 6 = 108.
9. What is the formula to calculate combinations as mentioned in Chapter 7 of Class 11 Maths?
The formula that you use to calculate the total number of combinations of ‘n’ number of different things taken ‘r’ at a time, indicated by nCr, is given by nCr = n!r! (n - r)!, where 0 r n. By using this simple formula, you can calculate combinations. If you are looking for more solutions from this chapter, check out the NCERT Solutions for Chapter 7 of Class 11 Maths on Vedantu.