Test Index

Probability Part 2

Section: Mathematics

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Question : 77 of 100

Marks: +1, -0

The probability that a randomly chosen one-one function from the set

\{a, b, c, d\}

\{1,2,3,4,5\}

f(a)+2 f(b)

-f(c)=f(d)

[28-Jun-2022-Shift-2]

$\;\frac{1}{24}$
$\;\frac{1}{40}$
$\;\frac{1}{30}$
$\;\frac{1}{20}$

Solution:

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)+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)

\therefore n(E)=6

\therefore

Required probability

=\;\frac{n(E)}{n(S)}=\;\frac{6}{120}=\;\frac{1}{20}

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