A monkey is given 12 blocks : 3 shaped like squares, 3 rectangles, 3 triagles and 3 circles. if it draws three of each kind in order-say 3 triangles,then 3 squares, and so on-would you suspect that the monkey associates identically shaped figures? Calculate the propability of this event.

Question

misty1212 · Answer

HI!!

misty1212 · Answer

nice shoes!

misty1212 · Answer

we can calculate the probability of 3 triangles, 3 squares, then 3 rectangles first 
then multiply that result by 6, since it could be 
TSR
TRS
STR
SRT
RTS
RST

misty1212 · Answer

first is a triangle $\frac{3}{12}$ 
second is a triangle $\frac{2}{11}$
third is a triangle $\frac{1}{10}$
fourth is a rectangle $\frac{3}{9}$ 
fifth is a rectangle $\frac{2}{8}$ 
etc

misty1212 · Answer

the pattern should be pretty clear
when you multiply these you will get 
$$\frac{3\times 3!}{12!}$$

misty1212 · Answer

since there are 6 ways to do it, as above, final answer (if i am reading it right) is 
$$\frac{6\times 3\times 3!}{12!}$$which is easy enough to compute

misty1212 · Answer

can i get the shoes now?

anonymous · Answer

hahah thank you :) 
well  i dont know about the shoes but you are sure getting best response :p

misty1212 · Answer

$$\color\magenta\heartsuit$$

anonymous · Answer

okay i am actually going through the problem and I dont think that is the solution :/