NCERT solution Class 11 permutations and combinations

NCERT Solutions

Class 11 Maths

Permutations and Combinations

NCERT Questions

Ex.7.1 Q.1
Ex.7.1 Q.2
Ex.7.1 Q.3
Ex.7.1 Q.4
Ex.7.1 Q.5
Ex.7.2 Q.1
Ex.7.2 Q.3
Ex.7.2 Q.2
Ex.7.2 Q.4
Ex.7.2 Q.5
Ex.7.3 Q.1
Ex.7.3 Q.2
Ex.7.3 Q.3
Ex.7.3 Q.4
Ex.7.3 Q.5
Ex.7.3 Q.6
Ex.7.3 Q.7
Ex.7.3 Q.8
Ex.7.3 Q.9
Ex.7.3 Q.10
Ex.7.3 Q.11
Ex.7.4 Q.1
Ex.7.4 Q.2
Ex.7.4 Q.3
Ex.7.4 Q.4
Ex.7.4 Q.5
Ex.7.4 Q.6
Ex.7.4 Q.7
Ex.7.4 Q.8
Ex.7.4 Q.9
Ex.Misc.Q.1
Ex.Misc.Q.1
Ex.Misc.Q.3
Ex.Misc.Q.4
Ex.Misc.Q.5
Ex.Misc.Q.6
Ex.Misc.Q.7
Ex.Misc.Q.8
Ex.Misc.Q.9
Ex.Misc.Q.10
Ex.Misc.Q.11

Ex.7.3 Q.11

In how many ways can the letters of the word PERMUTATIONS be arranged if the

(1) words start with P and end with S,

(2) vowels are all together,

(3) there are always 4 letters between P and S?

In the word PERMUTATIONS, there are 2 Ts and all the other letters appear only once.

(1) If P and S are fixed at the extreme ends (P at the left end and S at the right end), then 10 letters are left.

Hence, in this case, required number of arrangements = 10! ÷ 2! = 1814400

(2) There are 5 vowels in the given word, each appearing only once.

Since they have to always occur together, they are treated as a single object for the time being.

This single object together with the remaining 7 objects will account for 8 objects.

These 8 objects in which there are 2 T’s can be arranged in 8! ÷ 2! ways.

Corresponding to each of these arrangements, the 5 different vowels can be arranged in 5! ways.

Therefore, by multiplication principle, required number of arrangements in this case = 8! ÷ 2! × 5 = 2419200

(3) The letters have to be arranged in such a way that there are always 4 letters between P and S.

Therefore, in a way, the places of P and S are fixed. The remaining 10 letters in which there are 2 T’s can be arranged in 10! ÷ 2! ways.

Also, the letters P and S can be placed such that there are 4 letters between them in 2 × 7 = 14 ways.

Therefore, by multiplication principle, required number of arrangements in this case = 10! ÷ 2! × 14 = 25401600

Video solution:

Permutations and Combinations Class 11 Maths NCERT Chapter 6 NCERT Solutions

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Attempt to Solve Yourself: Before looking at the solution, try to solve or answer the question independently. This practice will help you test your knowledge and problem-solving skills.
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Refer to Solution Video (if needed): If you encounter difficulty or are unable to solve a question, you can refer to the NCERT solution video on Permutations and Combinations Class 11 Maths NCERT Chapter 6 to get a step-by-step explanation of the correct approach. Pay attention to the reasoning and methodology used in the video.
Solve Again Yourself: Once you've understood the solution, attempt to solve the question again by yourself. Repetition and practice solidify your understanding of the concepts and improve retention.
Avoid Memorization: Focus on understanding the underlying principles and concepts behind each solution. Avoid simply memorizing the solutions, as this may hinder your ability to apply the knowledge in different contexts.
Attempt All Questions: Make an effort to attempt all the questions provided in the NCERT textbook. This comprehensive practice will help you cover the entire syllabus and reinforce your understanding across various topics. You may refer Class 11 Maths Permutations and Combinations Online Test on LearnoHub.com.
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NCERT solutions of Permutations and Combinations Class 11 Maths - all questions of all exercises are solved. Q. No. 1, 2, 3, and so on. Complete explanation and detailed solution makes them the best videos for Class 11 Maths Permutations and Combinations NCERT solutions.