<bosons>

○○○○○○○○○○ (num of balls=10)

UUUUUU (num of boxes=6)

assuming that one can put any number of indistinguishable balls into one box

eg : putting the 3 balls into the first box,

the 3 balls of the rest into the forth one, and put the rest into the last one

⇔

○○○|||○○○||○○○○

⇔

15C5 = 15C10 = 6H10

in general, if num of balls = r, num of boxes = n, then (n+r-1)C(n-1) = (n+r-1)C(r) = nHr

<fermions>

○○○ (num of balls=3)

UUUUUUUUUU (num of boxes=10)

assuming that one can put only one ball into one box, what is called, the Pauli exclusion principle ( each ball indistinguishable )

eg : putting the one ball into the first box,

the one of the rest into the ninth one, and the last one into the last one

⇔

10C3

in general, if num of balls = r, num of boxes = n, then nCr

<classical particles>

(1)(2)(3) (num of balls=3)

UUUUUU (num of boxes=6)

assuming that all balls can go to any one of the six boxes

(each ball identical) all balls can take any one of the boxes.

⇔ repeated permutation, 6^3

in general, if num of balls = r, num of boxes = n, then n^r

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