Question

The probability that a randomly chosen one-one function from the set {a, b, c, d} to the set {1, 2, 3, 4, 5} satisfies f(a) + 2f(b) - f(c) = f(d) is :

• A. $\frac{1}{24}$
• B. $\frac{1}{40}$
• C. $\frac{1}{30}$
• D. $\frac{1}{20}$

Answer 1

Answer: (D)

$\frac{1}{20}$

Answer 2

The correct answer is (D) : $\frac{1}{20}$
Number of one-one function from {a, b, c, d} to set {1, 2, 3, 4, 5} is
$^5P_4=120 n(s)$
The required possible set of value (f(a), f(b), f(c), f(d)) such that f(a) + 2f(b) – f(c) = f(d) are (5, 3, 2, 1), (5, 1, 2, 3), (4, 1, 3, 5), (3, 1, 4, 5), (5, 4, 3, 2) and (3, 4, 5, 2)
∴ n(E) = 6
∴ Required probability
$=\frac{n(E)}{n(S)}=\frac{6}{120}=\frac{1}{20}$