5. if there are 7 swimmers in a race, in how many different orders can they finish (assuming there are no…

to arrange 7 swimmers in order. The formula for permutations of ( n ) distinct objects is ( n! ) (n factorial), which is ( n\times(n - 1)\times(n - 2)\times\cdots\times1 ). Here, ( n = 7 ), so we need to calculate ( 7! ).

Step2: Calculate ( 7! )

( 7! = 7\times6\times5\times4\times3\times2\times1 ) First, ( 7\times6 = 42 ) Then, ( 42\times5 = 210 ) Next, ( 210\times4 = 840 ) Then, ( 840\times3 = 2520 ) Next, ( 2520\times2 = 5040 ) Finally, ( 5040\times1 = 5040 )

Answer:

( 7! = 5040 )