2016 is absolutely awesome 13

A total of 2016 tickets, numbered 1, 2, 3, 4, ... , 2015, 2016, are placed in an empty bag.

Alberto removes ticket x x from the bag. Beck then removes ticket y y from the bag. Finally, Chris removes ticket z z from the bag.

They notice that x < y < z x<y<z and x + y + z = 6000 x+y+z=6000 . In how many ways could this happen?

The answer is 192.

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1 solution

Parmeshwar Sharma
Dec 26, 2015

x+y+z =6000
X+Y+Z=48 ( taking X as 2016- x same has been done for y and z )
Which gives u 50c2 =1225
Now cases where X and Yare same
2X + Z =48 ( 25 cases where Z is an even no till 48)
( similarly we have 2 more cases when X and Z are equal and when Y and Z are equal)

Also the case where all X,Y,Z are same (16 each, but this case has been counted 3 times so we need to balance hence
1225-25*3 +2 = 1152
In this all 3 are unequal and one sixth of the cases will give u when. X< Y<Z will happen

Hence 1152/6= 192
Hence the solutiom

No answer is 147

Dinesh Ram - 5 years, 5 months ago

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