Four people P, Q, R and S have to sit on the four stools marked 1, 2, 3 and 4.
P goes and sits down on stool 4. Q does not want to sit on a stool that is immediately next to P's. Keeping this in mind, in how many different ways could Q, R and S arrange themselves on the remaining stools?
Answers
Given : Four people P, Q, R and S have to sit on the four stools marked 1, 2, 3 and 4.
P goes and sits down on stool 4
Q does not want to sit on a stool that is immediately next to P's.
To Find : in how many different ways could Q, R and S arrange themselves on the remaining stools
Solution:
Assumed that Stools are arranged in order are in a straight line
1 2 3 4
P
As P sits on 4th Stool
Hence 3 persons Q R S can sit on 3 stools in
3! = 6 Ways
if Q sits on stool 3 ( which is not allowed)
then remaining 2 can sit in 2! = 2 Ways
Hence Total Possible arrangement when P sits on 4 and Q does not sit immediately next to P
= 6 - 2
= 4 ways
1 2 3 4
Q R S P
Q S R P
R Q S P
S Q R P
4 possible arrangements
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