## Task B-4.4.

Ana has glasses with black, brown, green, red, yellow, and blue frames. On Saturdays and Sundays, she always wears glasses with black or brown frames. Of the remaining five days, she wears a green frame at least three times, while on the other days she wears glasses with red, yellow, or blue frames. In how many different ways can Ana arrange the weekly combination of glasses frame colors? Ana does not change the frame of her glasses during the day.
## Solution.

For Saturday and Sunday, Ana can choose glasses in $2 \cdot 2=4$ ways.

For the remaining 5 days, we distinguish the following cases:

1. The green frame is worn exactly three days.

First, we choose three days for the green frame, which can be done in $\binom{5}{3}=10$ ways. For the remaining two days, we choose red, yellow, or blue frames, which can be done in $3^{2}=9$ ways. Thus, in this case, we have a total of $9 \cdot 10=90$ color combinations per day.

2. The green frame is worn exactly four days.

Four days for the green frame can be chosen in $\binom{5}{4}=5$ ways, and for the fifth day, the frame color can be chosen in 3 ways, which is a total of $5 \cdot 3=15$ ways.

3. The green frame is worn exactly five days.

This case has only one possible combination.

1 point

According to the above, for the middle five days, Ana has: $90+15+1=106$ combinations, which means she has a total of $4 \cdot 106=424$ weekly combinations.