Question

GMAT基础数学题，谢谢~ 希望牛人看看

Tofurnish a room in a model home, an interior decorator is to select 2 chairs and2 tables from a collection of chairs and tables in a warehouse that are alldifferent from each other. If there are5 chairs in the warehouse and if 150 different combinations are possible, howmany tables are in the warehouse?
(A) 6

(B) 8

(C) 10

(D) 15

(E) 30

答案是A

我把方程列出来了，可是不会解方程，有牛人点拨下吗，谢谢。

X!/2!(X-2)! = 15
X!/(X-2)! = 30
X(X-1)(X-2)! / (X-2)! = 30
X(X-1) = 30
X2 – X – 30 = 0
X2 – 6X + 5X – 30 = 0
X(X – 6) + 5(X – 6) = 0
(X – 6) (X + 5) = 0
X = 6 or X = -5
Negative value is not possible since we are calculating the number of tables
Therefore X = 6
Hence “A” is the answer

X(X-1)(X-2)! / (X-2)! = 30 是怎么从X!/(X-2)! = 30 变过来的哦？
X!怎么就变成了x(x-1)了？

Answer 1

X(X-1)【(X-2)!】 / (X-2)! = 30

这样更规范
约分后 就剩下x(x-1)=60了

追问

不对呀，是X(X-1)=30
我不明白X!怎么就变成了x(x-1).
请教~

追答

打错 是30 O(∩_∩)O~

只能说 X!变成了X(X-1)【(X-2)!】

即X!=X(X-1)【(X-2)!】
比如5！=5乘以4乘以3！ 一样

Answer 2

x! = x(x-1)(x-2)......1
（x-2)!=(x-2)(x-1).....1
相除不就把共同部分（x-2)(x-3)...1 约去了嘛
变成x(x-1)=30