Question

3. There are 9 lights labeled 1 to 9, and they are lined up in a row in Boelter Hall. For we can't turn off 2 lights that are next to each other or 3 lights in a row, and we can't turn off the first and the last lights in the row. How many ways are there to turn off 3 lights? budget reasons, we are going to turn off 3 of them. For security purposes

Answer 1

23 4 6 8 Gtiven that theve ave q lights labeled I to that osue lined up in a socu Ουγ aim is to select 3 lights to turn off so that no tuwo oP them asHe adjacent to each othest Gtiven the Prst and last lights can't be tuhmed ofp So discasidandlights So, numbest of lights semaining - 7 Suppose, i 3 lights aste selected to tusn off then (4-3)4 lights osie not selected Now theste aste 5 spaces betuveen these 4 lights indicated by # symbol (not selected) ue select any of thesee # symbols to be assigned to the light positions which aote to be tuisned off then we can tuusn off 3 lights that oste not adjacent to each othest. No of waye321 5! 312 to tuon of three lights 10 cooys