If four items are chosen at random without replacement from seven items, in how many ways can the four items be arranged, treating each arrangement as a different event (i.e., if order is important)?
A)35
B)840
C)5040
D)24

Question

Quizplus · Accepted Answer

First, choose 4 items out of 7, which can be done in 7C4 ways (combination formula: 7! / [4!(7-4)!] = 35 ways). Then, arrange these 4 items, which can be done in 4! (factorial) ways = 24 ways. Multiplying these together gives 35 * 24 = 840 ways.

If Four Items Are Chosen at Random Without Replacement from Seven