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TMUA 2020 · Paper 1 · Question 13 of 20

TMUA 2020 Paper 1 Question 13

Sequences and series — Expanding a trinomial · counting arrangements. Try it first; the answer and a full worked solution are below.

TMUA 2020 · Paper 1Sequences and seriesExpanding a trinomial · counting arrangements6 options
Find the coefficient of x2y4 in the expansion of (1 + x + y2)7.
  1. A6
  2. B10
  3. C21
  4. D35
  5. E105
  6. F210
Show the answer and worked solution
answer · F
  1. A6
  2. B10
  3. C21
  4. D35
  5. E105
  6. F210
Think of the expansion as choosing one of the three terms from each of the seven brackets. To end up with x2y4 you must take x from exactly two brackets, y2 from exactly two, and 1 from the remaining three. The number of ways to do that is 7!2! 2! 3! = 504024 = 210, and each contributes a coefficient of 1. Choosing only the y2 positions, (72) = 21, or only the x positions is the common slip.