Question

The number of ways $7plus(+)$ signs and $5minus(-)$ signs can be arranged in a row so that no two minus $(-)$ signs are together is

• A. $21$
• B. $35$
• C. $56$
• D. $28$

Answer 1

Answer: (C)

$56$

If we place all ${}^{\prime }{+}^{\prime }$ signs in a straight line first, there will be total $8$ places for ${}^{\prime }{-}^{\prime }$ signs so that no two of them are together. (either in between any two $+$ signs or at the extreme ends).
Out of $8$ places any $5$ places for ${}^{\prime }{-}^{\prime }$ signs can be selected in ${}^8{C}_5$ ways
$=56$ ways
Hence, option 'C' is correct.