11 players of the Indian cricket team are sitting at a circular table. The number of ways they can sit so that two players, the wicket keeper and the captain never sit together is ___

Step-by-step solution

Total number of players is 11 . Total number of ways to arrange 11 players around a circular table is (11 - 1)! = 10! . To find the number of ways where the wicket keeper and the captain sit together, consider them as a single unit. The number of units to arrange is 9 remaining players plus 1 unit, which equals 10 units. The number of ways to arrange these 10 units around a circular table is (10 - 1)! = 9! . The wicket keeper and the captain can interchange their positions within the unit in 2! = 2 ways. The number