# The total number of ways in which six '+' and four '-' signs can be arranged in a line such that no two signs '-' occur together, is ……….. .

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Solution :
The arrangement can be understand with the help of following figure. <br> {:(-, +, -, +, -, +, -, +, -, +, -, +,-):} <br> Thus, '+' sign can be arranged in 1 way because all are identical. <br> and 4 negative signs can be arranged at 7 places in ""^(7)C_(4) ways. <br> therefore total number of ways = ""^(7)C_(4) xx 1 <br> = (7"!")/(4"!"3"!") = (7 xx 6 xx 5 xx 4"!")/(3"!" xx 4"!") <br> = (7 xx 6 xx 5)/(3 xx 2 xx 1) = 35 ways
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