Let A = {1, 2, 3, 4, 5, 6}. The number of one-one functions f : A A such that , and f(2) + f(3) = 5, is ________. [2026]

Question

Let A = {1, 2, 3, 4, 5, 6}. The number of one-one functions f : A $\to$ A such that $f (1) \geq 3, f (3) \leq 4$ , and f(2) + f(3) = 5, is ________. [2026]

Smart Achievers · Accepted Answer

(72)

A = {1, 2, 3, 4, 5, 6}

f : A $\to$ A

Case I : (f(2), f(3)) = (4, 1) or (1, 4), then Choices of values of f(1) $\in$ {3, 5, 6} = 3

Number of ways 2 x 3 x 6 = 36

Case II : (f(2), f(3) = (2, 3) or (3, 2), then Choices of values f(1) $\in$ {4, 5, 6} = 3

Number of ways = 2 x 3 x 6 = 36

Total number of functions = 36 + 36 = 72.

Solution

Q.
Let A = {1, 2, 3, 4, 5, 6}. The number of one-one functions f : A $\to$ A such that $f (1) \geq 3, f (3) \leq 4$ , and f(2) + f(3) = 5, is ________. [2026]

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Solution

Q. Let A = {1, 2, 3, 4, 5, 6}. The number of one-one functions f : A → A such that f(1)≥3, f(3)≤4, and f(2) + f(3) = 5, is ________. [2026]

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Q.
Let A = {1, 2, 3, 4, 5, 6}. The number of one-one functions f : A $\to$ A such that $f (1) \geq 3, f (3) \leq 4$ , and f(2) + f(3) = 5, is ________. [2026]