Question

How many different arrangements can be made with ten pieces of silverware laid in a row if three are identical spoons, four are identical forks, and three are identical knifes

Answer 1

10 pieces of silverware laid in a row if 3 are identical spoons, 4 are identical forks, and 3 are identical knifes

The arrangement of 'm' objects on which 'n' objects are of same kind is
`(m!)/(n!)`

Given: 10 pieces of silverware so its 10!

3 are identical spoons so its 3!

4 are identical forks so its 4!

and 3 are identical knifes so its 3!

Arrangements made =
`(10!)/(3!*4!*3!)` = 4200