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Glass Balls

Answer :

There are, in all, sixteen balls to be broken, or sixteen places in the order of breaking. 
Call the four strings A, B, C, and D—order is here of no importance. 
The breaking of the balls on A may occupy any 4 out of these 16 places—that is, the combinations of 16 things, taken 4 together, will be

13 × 14 × 15 × 16  = 1,820
1 × 2 × 3 × 4

ways for A. In every one of these cases B may occupy any 4 out of the remaining 12 places, making

9 × 10 × 11 × 12  = 495
1 × 2 × 3 × 4

ways. Thus 1,820 × 495 = 900,900 different placings are open to A and B. But for every one of these cases C may occupy

5 × 6 × 7 × 8  = 70
1 × 2 × 3 × 4

different places; so that 900,900 × 70 = 63,063,000 different placings are open to A, B, and C. 
In every one of these cases, D has no choice but to take the four places that remain. 
Therefore the correct answer is that the balls may be broken in 63,063,000 different ways under the conditions. 




Math Genius