Two numbers x & y are chosen at random (without replacement) from set {1, 2, 3, ......, 1000} .

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14.Probability

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Two numbers $x$ $\&$ $y$ are chosen at random (without replacement) from the set $\{1, 2, 3, ......, 1000\}$. Then the probability that $|x^4 - y^4|$ is divisible by $5$, is -

A

$\frac{113}{999}$

B

$\frac{400}{999}$

C

$\frac{679}{999}$

D

$\frac{1}{999}$

Solution

Sample space $=\,^{1000} \mathrm{C}_{2}=500 \times 999$

$\{1,2,3,4,6, \dots \dots\}$

and $\{5,10,15,20, \dots \dots\}$

first first set select any two numbers or from

second set select any two numbers $\,^{800} \mathrm{C}_{2}+\,^{200} \mathrm{C}_{2}$

$=400 \times 799+100 \times 199=100(3196+199)$

$=3339500$

Standard 11

Mathematics

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