Use generalized counting principle.

Explanation:

We have 10 digits to choose from {0,1,2,3,4,5,6,7,8,9} for slot A

Then after making that first selection, there are 10-1 = 9 choices left for slot B

Then for slot C, there are 10-2 = 8 choices

Finally for slot D, there are 10-3 = 7 choices

We have a steady countdown: 10,9,8,7

Overall, there are 10*9*8*7 = 5040 different permutations

Order matters because a code like 1234 is different from 4321

Alternative Method:

We can use the nPr permutation formula with n = 10 and r = 4

nPr = (n!)/((n-r)!)

10P4 = (10!)/((10-4)!)

10P4 = (10!)/(6!)

10P4 = (10*9*8*7*6!)/(6!)

10P4 = 10*9*8*7

10P4 = 5040

and we get the same result.

8

step-by-step explanation:

to find the amount of gift bags to use all the supplies, find the gcf or greatest common factor. this is the largest number which multiplies evenly into each term.

48 has factors: 1, 2, 3, 4, 6, 8, 12. 16, 24, 48

80 has factors: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80

64 has factors: 1, 2, 4, 8, 8, 16, 32, 64

the highest number factor they all share in common is 8. this means there will be 8 bags with 6 pencils, 10 markers, and 8 stickers in each bag.