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Chapter 13: Q. 51 (page 856)

Forming Words How many different 9-letter words (real or imaginary) can be formed from the letters in the word ECONOMICS?

Short Answer

Expert verified

The possible number of words is 90720.

Step by step solution

01

Step 1. Given information.

The given word is "ECONOMICS".

Each word formed will have 9 letters: 2 C's, 2 O's, 1 E, 1 N, 1 M, 1 I, and 1 S.

02

Step 2. Concept.

The number of permutations of nobjects of which n1are of one kind, are of a second kind, ..., and nkare of a kthkind is given by

n!n1!路n2!路鈰�路nk!

Where n=n1+n2+鈰�+nk.

03

Step 3. Determine the number of possible words.

Using the above concept, we get

Possible words=9!2!路2!路1!路1!路1!路1!路1!=9路8路7路6路5路4路3路2!2!路2路1路1路1路1路1路1=90720

The possible number of words is 90720.

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