If f: A arrow B is an injective mapping such that f ( i ) ≠ i and A = 1,2,3,4 B = 1,2,3,4,5 then number of such mapping are

Question

If f: A arrow B is an injective mapping such that f ( i ) ≠ i and A = 1,2,3,4 B = 1,2,3,4,5 then number of such mapping are (A) 53 (B) 52 (C) 44 (D) None of these

Tardigrade Admin · Accepted Answer

5 C 4 ⋅ 4 !-[ 4 C 1 × 4 C 3 × 3 !- 4 C 2 × 3 C 2 × 2 !+ 4 C 3 ⋅ 2 C 1 ⋅ 1- 4 C 4] 120-96+36-8+1 ⇒ 24+28+1 ⇒ 53

Q. If $f : A \to B$ is an injective mapping such that $f (i) \neq = i$ and $A = {1, 2, 3, 4}, B = {1, 2, 3, 4, 5}$ then number of such mapping are

53

52

44

None of these

$^{5} C_{4} \cdot 4! - [^{4} C_{1} \times^{4} C_{3} \times 3! -^{4} C_{2} \times^{3} C_{2} \times 2! +^{4} C_{3} \cdot^{2} C_{1} \cdot 1 -^{4} C_{4}]$
$120 - 96 + 36 - 8 + 1 \Rightarrow 24 + 28 + 1 \Rightarrow 53$

Q. If f:A→B is an injective mapping such that f(i)=i and A={1,2,3,4},B={1,2,3,4,5} then number of such mapping are

53

52

44

None of these

5C4​⋅4!−[4C1​×4C3​×3!−4C2​×3C2​×2!+4C3​⋅2C1​⋅1−4C4​] 120−96+36−8+1⇒24+28+1⇒53

Q. If $f : A \to B$ is an injective mapping such that $f (i) \neq = i$ and $A = {1, 2, 3, 4}, B = {1, 2, 3, 4, 5}$ then number of such mapping are

$^{5} C_{4} \cdot 4! - [^{4} C_{1} \times^{4} C_{3} \times 3! -^{4} C_{2} \times^{3} C_{2} \times 2! +^{4} C_{3} \cdot^{2} C_{1} \cdot 1 -^{4} C_{4}]$
$120 - 96 + 36 - 8 + 1 \Rightarrow 24 + 28 + 1 \Rightarrow 53$