How many different letter arrangements can be made from the letters Fluke Propose Mississippi Arrange

# How many different letter arrangements can be made from the letters Fluke Propose Mississippi Arrange

J
240 points

How many different letter arrangements can be made from the letters
(a) Fluke?
(b) Propose?
(c) Mississippi?
(d) Arrange?

How many
jeffp

8.7k points

Use the formula for a set for n objects of which some are indistinguishable from each other,

$$\frac{n!}{n_1!n_2! \ldots n_r! }$$

part (a)

All letters in this case are distinguishable so,

$$5!=120$$

part (b)

In this 7 letter word we have 2 letters P's, and 2 letter O's,

$$\frac{7!}{2! 2!}=1260$$

part (c)

In this 11 letter word we have 4 letter S's, 4 letter I's, and 2 letter P's,

$$\frac{11!}{4! 4! 2!}=34650$$

part (d)

In this 7 letter word we have 2 letters R's, and 2 letter A's,

$$\frac{7!}{2! 2!}=1260$$

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