Question

PG (120-121) 4.26 In how many ways can a fleet commander assign five ships to the first, second third, fourth, and fifth positions in a column of ten ships?

please show detailed work!

Answer 1

total number of ships = 10

we have to assign ships in a column, this means that replacement is not allowed

so, we can assign first place in 10 ways

second place in 9 ways (because 1st place is already assigned)

third place in 8 ways (because 2nd place is already assigned)

fourth place in 7 ways (because 3rd place is already assigned)

and

fifth place in 6 ways (because 4th place is already assigned)

therefore, total number of ways = 10*9*8*7*6 = 30240 ways