Question 13
In Wiffle Ball Toss, a player tosses $4$ balls, one at a time, onto a table with white, blue, yellow and red holes.
White scores $0$, blue $1$, yellow $2$ and red $4$ points. A total of at least $4$ wins a prize. For example, Yellow-Blue-White-Blue scores $2+1+0+1=4$ and wins; White-Blue-Blue-White scores $0+1+1+0=2$ and does not. Each toss lands in exactly one hole and there are at least $4$ holes of each colour. How many different colour sequences win a prize?
White scores $0$, blue $1$, yellow $2$ and red $4$ points. A total of at least $4$ wins a prize. For example, Yellow-Blue-White-Blue scores $2+1+0+1=4$ and wins; White-Blue-Blue-White scores $0+1+1+0=2$ and does not. Each toss lands in exactly one hole and there are at least $4$ holes of each colour. How many different colour sequences win a prize?