Question 169
There are four spade cards with numbers $1$, $2$, $3$, $4$, six heart cards with numbers $1$, $2$, $3$, $\ldots$, $6$ and eight diamond cards with numbers $1$, $2$, $3$, $\ldots$, $8$. Suppose you choose three cards, one from each group. How many possible choices are there if the total of the numbers on the chosen cards must be a multiple of $7$?