Use the factorial formula or the shorthand multiplication method (starting at , multiply consecutive decreasing integers).
Permutations are used only when the (e.g., specific seats, specific jobs like President, or specific positions on a shelf). lesson 6 homework practice permutations answers
[ _8P_5 = \frac8!(8-5)! = \frac8!3! = \frac403206 = 6,720 ] Use the factorial formula or the shorthand multiplication
| Problem | Problem Type | Answer | |---------|--------------|--------| | 1 | Arrange 5 of 8 books | ( _8P_5 = 6,720 ) | | 2 | 4-digit codes from 0-9 (no repeat) | ( 10 \times 9 \times 8 \times 7 = 5,040 ) | | 3 | Line up 4 students from 9 | ( _9P_4 = 3,024 ) | | 4 | President, VP, Treasurer from 12 | ( 12 \times 11 \times 10 = 1,320 ) | | 5 | Ways to schedule 3 songs from 10 | ( 10 \times 9 \times 8 = 720 ) | | 6 | Arrange letters of “MATH” | ( 4! = 24 ) | | 7 | 2-digit numbers from 3,5,7,9 (no repeat) | ( 4 \times 3 = 12 ) | | 8 | Arrange 6 photos in a row | ( 6! = 720 ) | | 9 | Choose a 3-person committee (order matters: pres, sec, treas) | ( 10 \times 9 \times 8 = 720 ) | | 10 | How many ways to arrange 7 flags on a pole? | ( 7! = 5,040 ) | = \frac8
Always ask, "Does the order matter?" if the answer is "No," you should be using combinations ( ) instead. Stopping too early: When calculating , ensure you multiply . Do not just stop at the first number. Confusing 0!: Remember that is mathematically defined as Summary Table for Quick Reference Problem Type Formula Style Arranging all items Arranging 5 books on a shelf ( Picking a top group Choosing 1st and 2nd from 10 ( Codes/Passwords nrn to the r-th power (if repeats allowed) A 3-digit PIN (