Question

There are $10$ trees between two stations $A$ and $B$. Three of them are to be cut down then the total number of ways so that no two trees are to be cut consecutively, is

• A. ${}^8{C}_3$
• B. ${}^7{C}_3$
• C. ${}^{10}{C}_3$
• D. ${}^9{C}_3$

Answer 1

The correct option is A ${}^8{C}_3$

$3$ trees to be cut $7$ left

Total no. of ways to cut $3$ trees $=$

Total no. of was to place $3$ trees

in the given gaps,

$=$ select $3$ gaps from $8$ $={}^8{C}_3$