There are (n r) different linear arrangements of n balls of which r are black and n-r are white. give a combinatorial explanation of this fact

Question

Mathematics

Luciano Forbes

17 December, 19:56

There are (n r) different linear arrangements of n balls of which r are black and n-r are white. give a combinatorial explanation of this fact

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Wendy Wilkinson · Answer 1

Linearly arranging r black balls and (n-r) white balls, can be considered as picking r places for the black balls among the n places, and the white ball would fill in the remaining places automatically.

That's why we use (n r)