I have deck of 30 cards. Each card has a single digit and a color. There are 3 possible colours: red, blue and green. There are 10 possible digits: 0 through 9 inclusive. There is one of each digit-colour combo. Suppose I choose 4 cards. How many ways can I choose 4 cards such that, when they are sorted, they are numerically adjacent (eg. \{red, 0 , red 1 , blue 2, red 3
}
). For this problem, 9 and 0 are numerically adjacent (eg. red 8 , blue 9 , green 0 , red 1
}
is valid).