# Ne'er give up!

Level pending

How many integer solutions are there to the equation

$$\sum _{ i=1 }^{ 12 }{ { x }_{ i } } \quad =\quad 264$$

$$(i)$$ with $${x}_{i} \geq 0$$?

$$(ii)$$ with $${x}_{1}, {x}_{2}, {x}_{3}......{x}_{7} \geq 2$$, $${x}_{8}, {x}_{9} \geq 6$$ and $${x}_{10}, {x}_{11}, {x}_{12} \geq 4$$?

Step 1 Add the answers of $$(i), (ii)$$ and multiply by $$39916800$$.

Step 2 Now, change the $$\times$$ sign with $$+$$ sign.(Don't change any other operator, this change has to be done when the term is without any fraction)