find the no. of ways in which 6'+' abd 4'-' signs can be arranged such that no 2 '-' signs occur together.

Hi Shubham,

Consider 6 + signs in a line like this.

 +  +  +  +  +  + 

Cleasrly this has 7 gaps (5 inbetween, and two at the sides).

So out of these 7 places, we can select 4 places in ⁷C₄ ways, and put the - signs so that they are not adjacent.

So total number of ways = ⁷C₄ = 35 ways.

Best Regards,

Ashwin (IIT Madras).