Question

The total number of ways in which six '+' and four '–' signs can be arranged in aline such that no two '–' signs occur together is ___________.

Answer 1

Number of '+' sign = 6 and Number of '−' sign = 4
After placing 6 '+' sign, there are 7 places for '−' sign.
Now, we need to select 4 sign out of 7 places
∴ The total number of ways of arranging signs
Such that no two '−' are together = ⁷C₄
$=\frac{7!}{4!3!}=\frac{7\times 6\times 5}{2\times 3}=35$