The probability that a randomly chosen one-one function from the set a, b, c, d to the set…

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 :

Accepted Answer

Number of one-one function from $\{a, b, c, d\}$ to set $\{1,2,3,4,5\}$ is ${ }^{5} P_{4}=120 n(s)$.

The required possible set of value (f(a), $f(b), f(c), f(d))$ such that $f(a)+2 f(b)-f(c)=f(d)$ are $(5,3,2,1),(5,1,2,3),(4,1,3,5),(3,1,4,5)$, $(5,4,3,2)$ and $(3,4,5,2)$

$	herefore n(E)=6$

$	herefore $ Required probability $=\frac{n(E)}{n(S)}=\frac{6}{120}=\frac{1}{20}$

Solutions · 1