Question: 2018 Winter Final - 6
Nick (your friendly TA) eats lots of bananas. During a period of 7 days, Nick eats a total of 25 bananas. A banana
schedule is a sequence of 7 numbers, whose sum is equal to 25, and whose numbers indicate the number
of bananas that Nick eats on each day. Three examples of such schedules are (3,2,7,4,1,3,5),
(2,3,7,4,1,3,5), and (3,0,9,4,1,0,8). How many banana schedules are there?
(a)
${31 \choose 7}$
(b)
${32 \choose 7}$
(c)
${31 \choose 6}$
(d)
${32 \choose 6}$