combinatorics - black and white balls

In how many ways we can set in row 7 white balls and 5 black balls so as any black ball was not in the neighborhood with blach ball.

thanks in advance

mapeciatko said:

In how many ways we can set in row 7 white balls and 5 black balls so as any black ball was not in the neighborhood with blach ball.

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This is a typical separation problem: seven white balls will separate 5 black balls.
The seven white balls create eight places to place a black ball:
\(\displaystyle \underline{~~~~~}w\underline{~~~~~}w\underline{~~~~~}w\underline{~~~~~}w\underline{~~~~~}w\underline{~~~~~}w\underline{~~~~~}w\underline{~~~~~}\)

Choose five of them \(\displaystyle \dbinom{8}{5}.\)