Question 762375: How many ways are there for four Cricketers, three Swimmers and two Athletes be stand in a line if the same type of sports persons stand together?
Answer by ramkikk66(644)   (Show Source):
You can put this solution on YOUR website! Since the people of one sport should stand together, let us consider all 4 cricketers as one unit C, 3 swimmers as one unit S, 2 Athletes as one unit A.
So we have 3 units which can be arranged in 3! or 6 ways.
(CSA, CAS, ASC, ACS, SCA, SAC)
(Note: The expression n! (read as n-factorial is evaluated as 1*2*3...*n.
3! = 1*2*3 = 6)
Moreover, within each unit, the players can stand in all possible permutations.
4 cricketers can stand in 4! = 24 ways
3 swimmers can stand in 3! = 6 ways
2 swimmers can stand in 2! = 2 ways.
Hence the total number of ways = 6*24*6*2 = 1728 ways.
Hope this helps.
:)
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