Because it does not specify that she has to choose one or two from each category all pieces of jewelry can be treated as choices in a combination set.
the formula for a combination is

where n is a total number of choices ( 11 )
and r is number chosen out of those choices (4)
so
C(11,4)= \frac{11!}{4!(11-4)!}
She has 330 possible choices to come home with 4 pieces of jewelry
1 1 1 2
2 -3 1 -11 -2R1 + R2 → R2
-1 2 -1 8 R1 + R3 → R3
1 1 1 2
0 -5 -1 -15 R2 ⇔ R3
0 3 0 10
1 1 1 2
0 3 0 10 -R3
0 -5 -1 -15
1 1 1 2
0 3 0 10 1/3 R2
0 5 1 15
1 1 1 2 -R2 + R1
0 1 0 10/3 -5R2 + R3
0 5 1 15
1 0 1 -4/3
0 1 0 10/3 -R3 + R1
0 0 1 -5/3
1 0 0 1/3
0 1 0 10/3
0 0 1 -5/3
Therefore, x = 1/3, y = 10/3, z = -5/3
X² - 10x = 46
10/2 = 5; 5²+ 25 add 25 to both sides
x² - 10x + 25 = 46 + 25
so the number you have to add to complete the square is 25.