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

Question

2 years ago

15

identical forks, and three are identical knifes

1 answer:

LuckyWell [14K] · Answer 1 · 2021-12-19T15:16:20+03:00

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 $\frac{m!}{n!}$

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 = $\frac{10!}{3!*4!*3!}$ = 4200