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 ……….. .

Explanation

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