Question 2
On the table there are $21$ cards, one with each of the integers from $1$ to $21$ inclusive.
Xavier selects $4$ cards and shows them to Ana. Then Ana takes one card away from Xavier (whichever she wants). If the sum of the numbers on the $3$ cards Xavier keeps is a multiple of $3$, Ana wins. Otherwise, Xavier wins.
Determine in how many ways Xavier can choose the $4$ cards so as to be sure of winning, no matter how well Ana plays.
(Two choices of the same $4$ cards in a different order are considered the same choice.)
Xavier selects $4$ cards and shows them to Ana. Then Ana takes one card away from Xavier (whichever she wants). If the sum of the numbers on the $3$ cards Xavier keeps is a multiple of $3$, Ana wins. Otherwise, Xavier wins.
Determine in how many ways Xavier can choose the $4$ cards so as to be sure of winning, no matter how well Ana plays.
(Two choices of the same $4$ cards in a different order are considered the same choice.)