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Question #41088

Difficulty: 8/10 | 🟢 Free

The Question

Let $A = \{1, 2, 3, 4, 5, 6, 7\}$ and $B = \{1, 2, 3, 4\}$ . Find the number of surjective functions $f: A \to B$ such that $f(1) \le f(2) \le f(3)$ .

Options

A.
2260
B.
2140
C.
2480
D.
2320

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Bridge

Practice problems that bridge the gap between foundational theory and advanced practical application.

Concepts Behind This Question

Inclusion-Exclusion Principle|Injective Mapping (One-One)|Equivalence Class Partitioning

Why This Question Is Tricky

Common Mistakes

This question tests the ability to combine order constraints with the Inclusion-Exclusion Principle for counting surjective functions.

A common trap is assuming the remaining elements can be mapped in a standard surjective way without accounting for the specific elements already covered by the constrained domain subset.

Students might incorrectly multiply the 20 non-decreasing sequences by a fixed number of surjective mappings, ignoring that the target requirements dynamically change based on the number of distinct values in the sequence.

Quick Facts About This Question

Question Information

Subject	Mathematics
Chapter	Probability - Class 11
Concept	Inclusion-Exclusion Principle
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free