Couple's Birthday Celebration
Probability
Level
2
8 people have to be seated in a row. Find the number of ways in which this can be done if person X and person Y must always sit together. Input your answer as sum of last 3 digits of number of ways.
The answer is 8.
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First, instead of trying to find the permutations of 8 people, think of X and Y to form a single entity.
The number of ways we can arrange A, B, C, D, E, F, {X, Y} is 7!
But then again X and Y can sit as (X,Y) or (Y,X). So, the number of ways we can arrange them all is 7 ! × 2 !
(The image in the problem shows the idea of grouping which I have used. If you have followed my solution, you should understand. Philosophically speaking, X and Y are so close and love each other that they are inseperable)