1: Make a table:
Prepare four lists, according to the number
of coupons selected and see that there are 14
(Note: Each time you choose three coupons, you
omit the fourth coupon. There are only four ways
that one coupon can be omitted. Using this gives
you a faster way to find the number of 3-coupon
2: Use the Counting Principle:
Megan must use either zero or one $8-coupon.
That is 2 possibilities. Similarly, there are
2 possible amounts using the $13-coupon ($0 or
$13), 2 possible amounts using the $17-coupon
($0 or $17), and 2 possible amounts using the
$22-coupon ($0 or $22). Together, there are 2
× 2 × 2 × 2 = 16 different sums that can be made.
However, this includes both $0 and the two ways
to make $30. Thus, there are 14 different sums
that can be made using at least one coupon.