Question

10 persons are sitting around a circle .in how many ways can 2 persons out of them can be selected so that they are not adjacent to eachother​

Answer 1

First find the total number of ways of selecting three people out of ten seated in a round table. Total number of selection is equal to

10

C

3

.

But the condition is that no two of them should be adjacent.

So first find the selections in which exactly two people are next to each other. Two people next to each other can be selected in 10 ways (AB,BC,CD,DE,EF,FG,GH,HI,IJ,JA). Once an adjacent pair of people selected, the remaining one person can be selected in 6 ways (so that he/she is not next to any of them).

So, total number of selections possible so that exactly two people are next to each other is equal to 10×6=60

Also number of selections in which three people are together is 10.

(ABC, BCD........)

Hence, selections in which no two people are next to each other = total selection − ( selections in which exactly two are together + selections in which all three are together)

=

10 C3 (60+10)

=120−70

=50

Answer 2

Answer:

35

Step-by-step explanation:

total no. of persons (n) = 10

the total no .of ways to select two persons in 10c2

the no. of ways to select adjacent in each other 10

req combination = total -adjacent

=10c2 - 10

=10x9/2x1 -  10

=45 - 10

=35