If two different numbers are taken from set left{ {0,1,2,3, ldots ,10} right} , then probability tha

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14.Probability

hard

If two different numbers are taken from the set $\left\{ {0,1,2,3, \ldots ,10} \right\}$, then the probability that their sum as well as absolute difference are both multiple of $4$, is

A

$\frac{7}{{55}}$

B

$\frac{6}{{55}}$

C

$\frac{{12}}{{55}}$

D

$\frac{{14}}{{55}}$

(JEE MAIN-2017)

Solution

Let $A \equiv \{ 0,1,2,3,4, \ldots ..,10\} $

${\rm{n}}({\rm{S}}) = {\,^{11}}{{\rm{C}}_2} = 55$ where $'S'$ denotes sample space

Let $\mathrm{E}$ be the given event

$\therefore {\rm{E}} \equiv \{ (0,4),(0,8),(2,6),(2,10),(4,8),(6,10)\} $

$\Rightarrow \mathrm{n}(\mathrm{E})=6$

$\therefore P(E)=\frac{n(E)}{n(S)}=\frac{6}{55}$

Standard 11

Mathematics

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