Name: Ronnie
Question: Three new students arrived in class. Teacher says there are 210 ways you can set. How many empty seats are there in the classroom? After new student are assigned seats, how many empty seats will remain? Hi Ronnie, Just to see how you would calculate this suppose that there were 4 empty seats. The first of the three students to arrive would have a choice of 4 seats. Whichever seat she chose the second student would have a choice of 3 seats. Thus the two students could seat themselves in 4 3 = 12 ways. Whatever seats they chose the third student could choose either of the 2 remaining seats so altogether the three students could seat themselves in The first of the three students to arrive would have a choice of 10 seats. Whichever seat she chose the second student would have a choice of 9 seats. Thus the two students could seat themselves in 10 9 = 90 ways. Whatever seats they chose the third student could choose any of the 8 remaining seats so altogether the three students could seat themselves in Try something between 4 and 10.
The method of "guess and check" is a perfectably reasonable way to solve this problem. At this point however you might see the pattern. If there are n(n - 1)(n - 2)
n so that
n(n - 1)(n - 2) = 210
n(n - 1)(n - 2) = 7 5 3 2
n has to be?
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