Suppose a soccer team decides to play with 5 defenders 3 mid

Suppose a soccer team decides to play with 5 defenders, 3 midfielders, and 2 forwards. How many ways can the eleven players on the field be assigned positions to play?

Solution

see we have total eleven players and 10 duties to be assigned

here 5 duties will be assigned and 3 midfielders duty and 2 forwards duty

therefore the total ways will be

5!*3!*2! = 1440 ways this can be done.