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Chapter 11: Problem 34

Use the formula for \({ }_{n} P_{r}\) to evaluate each expression. \({ }_{7} P_{3}\)

Short Answer

Expert verified
\({ }_{7} P_{3} = 210\)

Step by step solution

01

Identify n and r

From \({ }_{7} P_{3}\), we can infer that n = 7 and r = 3. So we will compute the permutation of 7 items taken 3 at a time.
02

Compute n! and (n-r)!

Compute 7! (7 factorial) and 4! (4 factorial). This means finding the product of all positive integers up to 7 and 4, respectively. So, 7! = 7*6*5*4*3*2*1 = 5040 and 4! = 4*3*2*1 = 24.
03

Use the permutation formula

Plug n = 7 and r = 3 into the permutation formula \({ }_{n} P_{r} = \frac{n!}{(n-r)!}\). Substituting, we get \({ }_{7} P_{3} = \frac{7!}{(7-3)!} = \frac{5040}{24}\)
04

Compute the final answer

Divide 5040 by 24 to get the final answer. So, \({ }_{7} P_{3} = 210\).

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