Question

10 persons are sitting in a row. In how many ways we can select three of them if adjacent persons are not selected

Answer 1

Hi there!
Here's the answer:

•°•°•°•°•°<><><<><>><><>°•°•°•°•

¶¶¶

If N objects are arranged (or) N people are sitting in a row. Then the number of ways of selecting r different objects so that none of objects (or) persons are next (or) adjacent to each other is :

$(n - r +1)_{C}__{r}$


PROOF :

If r persons are selected, then
(n - r) persons are left out, and the selections have to be made from the (n - r +1) Gaps.

•°• Total Possible ways = $(n - r +1)_{C}__{r}$

•°•°•°•°•°<><><<><>><><>°•°•°•°•

SOLUTION:

Given,

n = 10
r = 3
n - r +1 = 10 - 3 + 1 = 8

•°• Total possible ways = $8_{C}__{3}$

= (8 × 7 × 6)/(3×2)

= 56 ways.

•°•°•°•°•°<><><<><>><><>°•°•°•°•