[Fantasian]

My Nephew is into Tarot Cards. I am teaching him math. He asked me a question I have no idea how to answer. A new deck has 80 Cards in it, including 2 non-use cards. If we draw all 80 cards in a random order 1-80, what are the chance that we will not get any consecutive trump cards, of which there are 22.
In other words what are the chance that 22 specific cards will never come next to each other in a 1-80 card draw, where the cards are randomly drawn?

This is way out of my league...
Can you explain how this is arrived at?

Once again to clarify, If number 17 is a Special card, then neither the 16th nor 18th card can be another of the special cards.

Etc

Thank You

[ebaines]

With 80 cards, with 22 "specials" and no two specials may be next to each other:

1. The number of possible combinations of the 22 specials in the 80-card deck is C(80,22) - i.e. the combination of 22 out of 80 things.

2. The number of combinations that satisfy the criteria of no two specials being adjacent is C(59,22)

3. Hence the probability of this occurring is C(59,22)/C(80,22) = (58 x 57 x ...x 38)/(80 x 79 x 78 x ...x 60), which is approximately 0.000514.