If four vertices of a regular octagon are chosen at random, then probability that quadrilateral form

English

Gujarati

Hindi

14.Probability

hard

If four vertices of a regular octagon are chosen at random, then the probability that the quadrilateral formed by them is a rectangle is

A

$\frac{1}{8}$

B

$\frac{2}{{21}}$

C

$\frac{1}{{32}}$

D

$\frac{1}{{35}}$

Solution

(d) Here only $2$ rectangles are formed $ADEH, GFCB$.

$\therefore$ Number of favourable cases = $2$

and total number of cases ${ = ^8}{C_4}$

$\therefore$ Required probability $= \frac{2}{{^8{C_4}}}$$ = \frac{1}{{35}}$.

Standard 11

Mathematics

Share

Similar Questions

A committee consists of $9$ experts taken from three institutions $A, B$ and $C$, of which $2$ are from $A, 3$ from $B$ and $4$ from $C$. If three experts resign, then the probability that they belong to different institutions is

medium

Mr. $A$ has six children and atleast one child is a girl, then probability that Mr. $A$ has $3$ boys and $3$ girls, is –

normal

Out of $40$ consecutive natural numbers, two are chosen at random. Probability that the sum of the numbers is odd, is

easy

Twenty tickets are marked the numbers $1, 2, ….. 20.$ If three tickets be drawn at random, then what is the probability that those marked $7$ and $11$ are among them

easy

A three digit number is formed by using numbers $1, 2, 3$ and $4$. The probability that the number is divisible by $3$, is

medium