In the next Cricket World Cup T-20, Team T has decided to score 200 runs only through 4s and 6s. In how many ways can the Team T score these 200 runs? Choose the correct choice from the following choices
A) 13	B) 15	C) 16	D) 17	E) 18
Team T can score a maximum of 50 fours and a minimum of 2 fours with an interval or spacing of 3 units to accommodate the 6's.   So the number of fours scored forms an AP 2, 5, 8, ... 50 with a common difference of 3.   Number of ways of scoring 200 only through 4's and 6's = (50 - 2)/3 + 1= 
<gadget id="calculator">(50 - 2)/3 + 1</gadget>
<output>17</output>
17   Answer: D   Alternate solution: 4x + 6y= 200 --&gt; 2x + 3y = 100   x = (100 - 3y)/2 --&gt; 100 - 3y should be even. This is possible when 3y is even.   There are 17 even multiples of 3 between 0 and 100.   Answer: 17
<result>D</result>
In the next Cricket World Cup T-20, Team T has decided to score 200 runs only through 4s and 6s. In how many ways can the Team T score these 200 runs?