How many different letter arrangements can be made from the letters

(a) Fluke?

(b) Propose?

(c) Mississippi?

(d) Arrange?

How many

jeffp

Answered by Aaron 3 years ago

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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Asked: 3 years ago