Playing with ropes

Avik is holding six identical ropes in his hand where the mid portion of the rope is in his fist. The first end of the ropes is lying in one side, and the other ends of the rope are lying on another side. Kamrul randomly chooses the end points of the rope from one side, the tie every two of them together. And then he did the same thing for the other end. If the probability of creating a loop after tying all six rope is expressed as (a/b), (where a, b are coprime) find the value of (a+ b).

I want to know how to solve the problem. I tried but not sure of my answer.

#Combinatorics

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
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Comments

What have you tried?

Calvin Lin Staff - 4 years, 5 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$