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Set A has 3 elements and set B has 4 elements. The number of injections that can be defined from A to B is
- a)144
- b)12
- c)64
- d)24
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Set A has 3 elements and set B has 4 elements. The number of injection...
To find the number of injections (one-to-one mappings) from set A to set B, we can use the concept of permutations.
Permutations:
A permutation is an arrangement of objects in a specific order. In this case, we want to find the number of permutations of set B, where each element of set A is mapped to a distinct element in set B.
Formula for Permutations:
The number of permutations of a set with n elements is given by n!, which is the factorial of n. Factorial means multiplying all positive integers from 1 to n.
Number of Elements in Sets A and B:
Given that set A has 3 elements and set B has 4 elements.
Calculating the Number of Permutations:
To find the number of injections from A to B, we need to calculate the number of permutations of the 4-element set B, taking 3 elements at a time. This is denoted as P(4,3).
Using the formula for permutations, we have:
P(4,3) = 4!
= 4 × 3 × 2 × 1
= 24
Therefore, the number of injections that can be defined from set A to set B is 24.
Answer:
Hence, the correct answer is option 'D' (24).
Permutations:
A permutation is an arrangement of objects in a specific order. In this case, we want to find the number of permutations of set B, where each element of set A is mapped to a distinct element in set B.
Formula for Permutations:
The number of permutations of a set with n elements is given by n!, which is the factorial of n. Factorial means multiplying all positive integers from 1 to n.
Number of Elements in Sets A and B:
Given that set A has 3 elements and set B has 4 elements.
Calculating the Number of Permutations:
To find the number of injections from A to B, we need to calculate the number of permutations of the 4-element set B, taking 3 elements at a time. This is denoted as P(4,3).
Using the formula for permutations, we have:
P(4,3) = 4!
= 4 × 3 × 2 × 1
= 24
Therefore, the number of injections that can be defined from set A to set B is 24.
Answer:
Hence, the correct answer is option 'D' (24).
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Community Answer
Set A has 3 elements and set B has 4 elements. The number of injection...
No. of injections = 4P3 = 24
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Set A has 3 elements and set B has 4 elements. The number of injections that can be defined from A to B isa)144b)12c)64d)24Correct answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Set A has 3 elements and set B has 4 elements. The number of injections that can be defined from A to B isa)144b)12c)64d)24Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Set A has 3 elements and set B has 4 elements. The number of injections that can be defined from A to B isa)144b)12c)64d)24Correct answer is option 'D'. Can you explain this answer?.
Set A has 3 elements and set B has 4 elements. The number of injections that can be defined from A to B isa)144b)12c)64d)24Correct answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Set A has 3 elements and set B has 4 elements. The number of injections that can be defined from A to B isa)144b)12c)64d)24Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Set A has 3 elements and set B has 4 elements. The number of injections that can be defined from A to B isa)144b)12c)64d)24Correct answer is option 'D'. Can you explain this answer?.
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