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.4

Find the number of 4-digit numbers that can be formed using the digits 1, 2, 3, 4, 5 if no digit is repeated.

How many of these will be even?

4-digit numbers are to be formed using the digits, 1, 2, 3, 4, and 5.

There will be as many 4-digit numbers as there are permutations of 5 different digits taken 4 at a time.

Therefore, required number of 4-digit numbers = ⁵P₄ = 5! ÷ (5 – 4)!

= 5! ÷ 1!

= 5 × 4 × 3 × 2 × 1

= 120

Among the 4-digit numbers formed by using the digits, 1, 2, 3, 4, 5, even numbers end with either 2 or 4.

The number of ways in which units place is filled with digits is 2.

Since the digits are not repeated and the units place is already occupied with a digit (which is even),

the remaining places are to be filled by the remaining 4 digits.

Therefore, the number of ways in which the remaining places

can be filled is the permutation of 4 different digits taken 3 at a time.

Number of ways of filling the remaining places = ⁴P₃ = 4! ÷ (4 – 3)!

= 4! ÷ 1!

= 4 × 3 × 2 × 1

= 24

Thus, by multiplication principle, the required number of even numbers is 24 × 2 = 48

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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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.