A chef has 10 spice jars, but his new spice rack only holds 8 spice jars.

How many ways can he arrange 8 jars on the spice rack?

A.

45

B.

1,814,400

C.

80

D.

3,628,800

This is a statistics problem on permutation and combination. To differentiate this, permutation involves on the arrangement in which order doesn't matter. For combination, order matters.

For example, if you arrange A, B and C, for permutation it could be AB, BA, CA, AC, BC and CB. But for combination, it would just be AB, AC and BC.

So, in this problem where he is asked to arrange 8 jars in which order doesn't matter. It is permutation. You can solve this just by calculator. The formula would be nPr, where n is the total number of items while r is the number of items to be sorted. Thus,

nPr = 10P8 = 1, 814,400

Thus, the answer is B.