Book Maths Puzzle

In how many ways can seven '#' symbol and five '' symbol be arranged in a line so that no two '' symbols occur together?

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Book Other Question

Naresh has 10 friends and he wants to invite 6 of them to a party. How many times will 3 particular fiends never attend the party? In how many ways can 30 identical toys be divided among 10 boys if each boy must get at least one toy?