Question

tom and john are to sit in a row of 11 seats with 9 other people. how many ways are there for the 11 people to sit if tom sits to the left of john?

Answer 1

total number of ways of arrangement is 11!
now her either Tom is left of John or vice versa (only 2 optios)
hence the required number of ways tom sits to the left of john =11!/2

Answer 2

Total number of ways of arrangements for Tom to be left to John is 10! ways.
Here John has to be at a fixed position so that Tom is left to John.
Also, still with Tom left to John, the other 9 can be arranged in 9! ways.
Therefore total number of arrangements is 10! x 9! ways.