Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

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Short Answer

List all the ordered arrangements of 6 objects 1, 2, 3, 4, 5 and 6 choosing 3 at a time without repetition. What is $P (6, 3)$ ?

The list of ordered arrangements is:

123, 124, 125, 126, 132, 134, 135, 136, 142, 143, 145, 146, 152, 153, 154, 156, 162, 163, 164, 165, 213, 214, 215, 216, 231, 234, 235, 236, 241, 243, 245, 246, 251, 253, 254, 256, 261, 263, 264, 265, 312, 314, 315, 316, 321, 324, 325, 326, 341, 342, 345, 346, 351, 352, 354, 356, 361, 362, 364, 365, 412, 413, 415, 416, 421, 423, 425, 426, 431, 432 435, 436, 451, 452, 453, 456, 461, 462, 463, 465, 512, 513, 514, 516, 521, 523, 524, 526, 531, 532, 534, 536, 541, 542, 543, 546, 561, 562, 563, 564, 612, 613, 614, 615, 621, 623, 624, 625, 631, 632, 634, 635, 641, 642, 643, 645, 651, 652, 653, 654.

The value of the given permutation is 120.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information.

3 objects are chosen from 6 objects 1, 2, 3, 4, 5, and 6 at a time without repetition.

The given permutation is $P (6, 3)$ .

Step 2. Determine the list of ordered arrangements.

The list of ordered arrangements is:

123, 124, 125, 126, 132, 134, 135, 136, 142, 143, 145, 146, 152, 153, 154, 156, 162, 163, 164, 165,

213, 214, 215, 216, 231, 234, 235, 236, 241, 243, 245, 246, 251, 253, 254, 256, 261, 263, 264, 265,

312, 314, 315, 316, 321, 324, 325, 326, 341, 342, 345, 346, 351, 352, 354, 356, 361, 362, 364, 365,

412, 413, 415, 416, 421, 423, 425, 426, 431, 432 435, 436, 451, 452, 453, 456, 461, 462, 463, 465,

512, 513, 514, 516, 521, 523, 524, 526, 531, 532, 534, 536, 541, 542, 543, 546, 561, 562, 563, 564,

612, 613, 614, 615, 621, 623, 624, 625, 631, 632, 634, 635, 641, 642, 643, 645, 651, 652, 653, 654.

Step 3. Determine the value of permutation.

We know that,

$P (n, r) = \frac{n!}{(n - r)!}$

Using the above formula, we get

$\begin{array}{rcl} P (6, 3) & = & \frac{6!}{(6 - 3)!} \\ = & \frac{6!}{3!} \\ = & \frac{6 \times 5 \times 4 \times 3!}{3!} \\ = & 120 \end{array}$

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

List all the ordered arrangements of 6 objects 1, 2, 3, 4, 5 and 6 choosing 3 at a time without repetition. What is $P (6, 3)$ ?

Step by Step Solution

Step 1. Given information.

Step 2. Determine the list of ordered arrangements.

Step 3. Determine the value of permutation.

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

List all the ordered arrangements of 6 objects 1, 2, 3, 4, 5 and 6 choosing 3 at a time without repetition. What is P(6,3)?

Step by Step Solution

Step 1. Given information.

Step 2. Determine the list of ordered arrangements.

Step 3. Determine the value of permutation.

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List all the ordered arrangements of 6 objects 1, 2, 3, 4, 5 and 6 choosing 3 at a time without repetition. What is $P (6, 3)$ ?