Problem Solving (PS) | Re: How many different arrangements to seat four spectators in four of sev

Let's say the 4 spectators are A,B,C,D. Can we assume that these arrangements are all different:
A,B,C,D,x,x,x
A,B,C,x,D,x,x
A,B,C,x,x,D,x
A,B,C,x,x,x,D

Assuming yes, my approach was to find the number of ways to arrange 4 ppl in 4 seats and the number of ways to select 3 out of 7 empty seats (order doesnt matter with empty seats). Multiplying the two will get me the answer.
# of ways to arrange 4 ppl: 4! = 24
# of ways to select 3 empty seats: 7C3 = 35
24 * 35 = 840

Answer: E

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