Question

1. King Arthur had a circular table built. He argued, since his knights were all 'noble and equal, no knight could boast of siting higher than his peers at the round table How many seating arrangements are possible at the round table when Arthur and his 7 knights met? Assume the King is equal to his knights and can occupy any seat. 2. Eight cards are drawn from a standard deck of 52 cards. How many hands contain exactly 3 hearts? hands

Answer 1

In a circular arrangement we first have to fix the position for the first person, which can be performed in only one way (since every position is considered same if no one is already sitting on any of the seats), also, because there are no mark on positions.

Now, we can also assume that remaining persons are to be seated in a line, because there is a fixed starting and ending point i.e. to the left or right of the first person.

Once we have fixed the position for the first person we can now arrange the remaining (8-1)!

= 7! = 5040