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  4. Total number of ways in which five '+' and three '-' signs can be arranged in a line such that no two '-' sign occur together is

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Q. Total number of ways in which five $'+'$ and three $'-'$ signs can be arranged in a line such that no two $'-'$ sign occur together is

AMUAMU 2013Permutations and Combinations

Solution:

$+ \,\, + \,\, +\,\, +\,\,+$
On fixing five positive signs, there are $6$ places for negative signs.
$\therefore$ Required number of ways $={ }^{6} C_{3}=20$