How many arrangements are there of 12 distinct items?

There are 479,001,600 arrangments of 12 distinct items.

Step-by-step explanation:

Arrangements of n items:

The number of possible arrangements of n itens is given by the factorial of n, that is:

12 items:

There are 479,001,600 arrangments of 12 distinct items.

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step-by-step explanation:

d = distance between moon and sun, which in this problem is the hypotenuse of a right triangle.  

the distance y is the side opposite to angle x in the right triangle.   use the definition of the sine function from basic trigonometry.

sin(x) = y/d ⇒

d = y/sin(x)

x= 149. 24+7=31. 180-31=149

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