Practice By Tag: Counting Solutions of Linear Equations

Question: 2019 Fall Final - 7

1 . Nick 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)

${32 \choose 6}$

(d)

${31 \choose 6}$