Tradition tells us that in certain rural areas of Russia the marriage of a young woman was determined as follows: The young woman held in her hand 6 ribbons by the middle, so that the tips were above and below the hand. The young suitor had to tie by pairs the 6 tips that went up, and then tie the 6 tips below, also by pairs. If the young man tied the 6 ribbons in a single circle, then the wedding would take place in less than a year.
a) What is the probability of forming a single circle if the ribbons were tied randomly?
My answer was: (6C2)(4C2)(2C2)/6! However, the answer is: (4C1)(2C1)/[(5C1)(3C1)]
Can someone please explain to me why?
I am using the formula for combinations, nCr = n! / (r! * (n - r)!), where n represents the number of items, and r represents the number of items being chosen at a time