MCQ
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 $f(a)+2 f(b)-f(c)=f(d)$ is
- A$\frac{1}{24}$
- B$\frac{1}{40}$
- C$\frac{1}{30}$
- ✓$\frac{1}{20}$
✓
Answer
Correct option: D.
$\frac{1}{20}$
d
$n ( s )=5_{ c _{4}} \times 4 !=120$
$n ( s )=5_{ c _{4}} \times 4 !=120$
| $f ( a )$ + | $2 f(b)$ = | $f ( c )$ + | $f ( d )$ |
| $5$ | $2 \times 1$ | $4$ | $4$ |
| $4$ | $2 \times 2$ | $3$ | $5$ |
| $1$ | $2 \times 3$ | $2$ | $5$ |
$n ( A )=2 \times 3=6$
$\therefore P ( A )=\frac{ n ( A )}{ n ( s )}=\frac{6}{120}=\frac{1}{20}$
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