# I am carrot +_+

**Discrete Mathematics**Level 4

There are \(286\) carrots of \(143\) different shades such that there are exactly \(2\) carrots of each shade. All of these carrots after treating with the machine, are filled in a bag.

There are \(11^n\) different compositions possible for this bag. Find \(n\).

**Details and Assumptions**:-

\(\bullet\) The carrots formed by multiplying one particular carrot are identical (due to magic of the multiplier).

\(\bullet\) The \(143\) different shades are well distinguishable, no 2 look alike.

This problem is a part of the set Vegetable Combinatorics