In his refrigerator, Mr. Hemingway has 3 cans of Coke, 4 cans of Pepsi, and 2 cans of Mountain Dew. He wishes to arrange them on one shelf. In how many different ways can he arrange the 9 cans? (Keep in mind, the 3 cans of Coke look identical; as do the 4 cans of Pepsi and the 2 cans of Mountain Dew.)

hello from mrbilldoesmath!

answer:

a(n) - a(n-1) -3

discussion:

this ones a bit interesting. given a(n) = 5 - 3n consider this:

a(n-1) = 5 - 3(n-1)

          = (5 - 3n) + 3             => but a(n) = 5 - 3n, the first term

          = a(n)   + 3                 => subtract 3 from both sides

a(n-1) -3 = a(n)  

or

a(n) - a(n-1) -3

you,

mrb