A game involves making a 3 by 3 grid with nine cards from a standard deck. You win if three cards in a row (horizontally, vertically, or diagonally) are the same denomination or are consecutive (in any order).

Question

What is the probability that there is exactly one winning set of consecutive cards?

Ans - about 0.1004

Explanation of process required!!!!!!!

Answer 1

the 1st eleven cards in a suite can start a 3-card consecutive set

each card can start 16 con. sets ... 4 suites each for the 2nd and 3rd cards

4 suites * 11 cards per suite * 16 sets per card = 704 con.sets

there are 52C3 possible 3-card sets ... 22100 sets
... probability of a set being consecutive ... 704 / 22100 = .03186
... probability of a set not being consecutive ... 1 - .03186 = 0.96814

there are 8 possible sets on the grid
... the probability of exactly one being consecutive is
... 8 * .96814^7 * .03186

doesn't seem to agree with the "answer" ... where did it come from?

Answer 2

Official answers - back of the book!!!! Is it incorrect?