How do we separate it?

Probability Level 4

Find the number of ordered quadruples $({ x }_{ 1 },\quad x_{ 2 },\quad { x }_{ 3 },\quad { x }_{ 4 })$ of positive odd integers that satisfy $\sum _{ i=1 }^{ 4 }{ { x }_{ i } } =2016$

The answer is 170698584.

1 solution

Otto Bretscher
Apr 2, 2016

If we write $x_i=2a_i+1$ , we need to count the non-negative integer solutions of $a_1+a_2+a_3+a_4$ $=1006$ . The answer is ${1009 \choose 3}=\boxed{170698584}$

How do we separate it?

The answer is 170698584.

1 solution

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