Answer to Question #113528 in Combinatorics | Number Theory for Shivam

Question

I have 3 red, 2 green, and 5 silver plates. In how many ways can I stack these so that no red plate appears on top of a silver plate.

Answer 1

Solution:

The number of methods can be calculated using combinatorial formulas:

10! /(2!3!5!)

10!/(2!3!5!) total number of permutations;

5⋅2 ways that on one of the silver lies 3 red and 2greens can be placed in different ways;

5 ⋅2 the ways that one of the silver ones has two red ones and 2 greens can be placed in different ways;

25 ⋅ 2 ways that one lies 2 red and the other 1 red and 2 greens can be placed in different ways;

10! /(2!⋅3!⋅ 5!) -10-10-50= 2090 ways;

Answer: 2090 ways.