Question 972095
12 balls
The only way I get the first one is to do the replacement AFTER the first three balls are drawn.  I took the question to mean there is replacement AFTER each draw.  The answer I got was double what is said.  IF I replace after the first three balls, NOT what the question is asking, I get the second line below.
(5/12)^3 * (7/12)^3=125/1728 * 343/1728

(5/12)(4/11)(3/10)  * (7/12)(6/11)(5.10)
(60/1320) (210/1320)=(1/22)(21/132)=(1/22)(7/44)=7/968.  

WITH REPLACEMENT, AND TRUE REPLACEMENT
(5/12)(4/11)(3/10) *(7/9)(6/8)(5/7)

60/1320 * 210/504
1/22*105/252=(1/22)*(35/84)=(1/22)(5/12)=5/264

THE SOLUTION TO THE SURVIVAL ONE I POSTED ALREADY AND NEEDS TO BE CORRECTED.  YOU NEED THE PROBABILITIES OF THE 60-65, 65-70,60-70 AND ALL THREE.  The first is 0.7*0.4*0.8=0.224; second is 0.3*0.4*0.2=;0.024;  third 0.7*0.6*0.2=0.084; all three 0.056=0.388