Q76 / 160 · AP EAMCET 2024 (19 May Shift 2) · Mathematics

Out of first 5 consecutive natural numbers, if two different numbers x and y are chosen at random, then the probability that $x^4-y^4$ is divisible by 5 is

  • A
    $\frac{2}{5}$
  • B
    $\frac{4}{5}$
  • Correct answer
    C
    $\frac{3}{5}$
  • D
    $\frac{1}{5}$

Solution

$\because$ We know, if two numbers $x$ and $y$ are choosen at random without replacement from the set $\{1,2,3,4, \ldots .$. $5 K\}$, then the probability that $x^4-y^4$ is divisible by 5 is $\frac{17 K-5}{5(5 K-1)}$ $\because \text { Given set }=\{1,2,3,4,5\} \Rightarrow K=1$ So, required probability $=\frac{17 \times 1-5}{5(5 \times 1-1)}=\frac{12}{5 \times 4}=\frac{3}{5}$.

Hence, the correct answer is option: 'C'.

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