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Chapter 11: Problem 48

How many arrangements can be made using four of the letters of the word COMBINE if no letter is to be used more than once?

Short Answer

Expert verified
There can be 840 different arrangements.

Step by step solution

01

Identify the Number of Items and Spaces

The word 'COMBINE' has 7 different letters and the exercise asks for arrangements of 4 letters. So, we have 4 spaces to fill with 7 different letters.
02

Apply Permutation Formula

The formula for permutation without repetition is given by \(P(n, r) = n! / (n-r)!\), where 'n' is the number of total available choices and 'r' is the number of selections to be made. Here, 'n' is 7 (the total number of distinct letters in 'COMBINE') and 'r' is 4 (the number of letters to select and arrange). Plug these values into the formula.
03

Calculation

Calculate \(P(7, 4)\) = \(7! / (7-4)!\) = \(5040 / 6\) = 840.

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