2019 AMC 10 A Problem 17

A child builds towers using identically shaped cubes of different color. How many different towers with a height 8 cubes can the child build with 2 red cubes, 3 blue cubes, and 4 green cubes? (One cube will be left out.)

(A) 24 (B) 288 (C) 312 (D) 1,260 (E) 40,320

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AMC 10 Preparation Volume 4 published December 18, 2015:

Example 15. A gardener plants eight trees out of three maple trees, two oak trees, and four birch trees in a row. How many ways are there?

(A) 1260 (B) 1240 (C) 1360 (D) 1480 (E) 1630