Multiple choice

Six cards are drawn one by one from a set of unlimited number of cards, each card is marked with numbers $-1, 0,$ or $1$. Number of different ways in which they can be drawn if the sum of the numbers shown by them vanishes is

  1. $111$
  2. $121$
  3. $141$

  4. none
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C Correct answer
Explanation

This is a multinomial coefficient problem. We need the number of ways to choose six numbers from {-1, 0, 1} such that their sum is 0. This is the coefficient of x^0 in (x^-1 + 1 + x)^6.

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