Logic Lab Slides nPr
nCr
n!
5!
0!
120
LOGIC LAB
Permutations & Combinations
Lab Objectives
01
Distinguish between Permutations (order matters) and Combinations (order doesn't matter).
02
Apply the \(nPr\) and \(nCr\) formulas to solve real-world word problems accurately.
03
Design original counting scenarios to demonstrate conceptual mastery.
Warm-up: Factorial Fire
5 MIN
3!
\(3 \times 2 \times 1\)
4!
\(4 \times 3 \times 2 \times 1\)
5!
\(5 \times 4 \times 3 \times 2 \times 1\)
CRITICAL REVIEW
What is the value of zero factorial?
0! = 1
Video Observation
15 MIN
Embedded media
Focus Problems
The Book Arrangement (7:31)
The Engineer Teams (11:15)
Watch For
"For a permutation, the order matters , but for a combination, the order does not matter ."
Main Activity: Scenario Sort
20 MIN
1 The Sorting Phase
Grab your pack of 10 Word Problem Cards . Sort them into two distinct piles:
PERMUTATIONS
Order Matters
COMBINATIONS
Group Selection
2 The Solving Phase
Once sorted, pick:
2 Problems from the Permutation pile2 Problems from the Combination pile
Show your work using the \(nPr\) or \(nCr\) formulas!
Lab Closure
Complete your Exit Ticket before leaving the lab today.
MISSION: Create 1 Original P & 1 Original C Problem
Remember: 0! = 1 | Order Matters = P | Groups = C
Logic Lab Formula Guide LOGIC LAB
Formula & Reference Guide
Name: ____________________________
Date: ___________
Permutations
Used when the ORDER MATTERS . Arrangements where position or rank is specific.
\[nPr = \frac{n!}{(n - r)!}\]
Keywords
Arrange Rank Position Schedule Code/PIN
Combinations
Used when the ORDER DOES NOT MATTER . Selecting a group or committee.
\[nCr = \frac{n!}{r!(n - r)!}\]
Keywords
Group Committee Team Selection Sample
\(n\)
Total available
\(r\)
Number selected
\(n!\)
Factorial Product
Calculator Operations
Factorials (!)
1. Type the number (e.g., 5)
2. Press MATH
3. Arrow right to PROB
4. Select option 4: !
nPr (Permutations)
1. Type total items (\(n\))
2. Press MATH → PROB
3. Select option 2: nPr
4. Type selection size (\(r\))
nCr (Combinations)
1. Type total items (\(n\))
2. Press MATH → PROB
3. Select option 3: nCr
4. Type selection size (\(r\))
The "0! Rule" Reminder
The video tutorial emphasized this: \(0!\) is mathematically defined as \(1\). If you see zero factorial in your denominator, don't worry—the problem isn't undefined!
Scenario Sort Cards CARD 01
The Student Council
A school club has 15 members . In how many ways can they elect a President , a Vice President , and a Secretary ?
P
C
Show Work on Back
CARD 02
The Review Committee
A school club has 15 members . In how many ways can they select a committee of 3 members to review the budget?
P
C
Show Work on Back
CARD 03
Movie Marathon
You have a list of 10 movies you want to watch. In how many ways can you rank your top 3 favorite movies?
P
C
Show Work on Back
CARD 04
Pizza Night
A pizza parlor offers 8 different toppings . How many ways can you choose 2 toppings for your pizza?
P
C
Show Work on Back
CARD 05
The Bookshelf
In how many ways can you arrange 5 different colored books on a shelf?
P
C
Show Work on Back
CARD 06
Smoothie Selection
You have a bowl with 10 different types of fruit . How many ways can you select 5 fruit to blend into a smoothie?
P
C
Show Work on Back
CARD 07
Security Code
How many unique 4-digit security codes can be created using the digits 0-9 if no digits are repeated?
P
C
Show Work on Back
CARD 08
Card Deal
In how many ways can you be dealt a hand of 4 cards from a standard deck of 52 cards ?
P
C
Show Work on Back
CARD 09
Roommate Chores
There are 6 different chores to be done. In how many ways can they be assigned to 6 specific roommates ?
P
C
Show Work on Back
CARD 10
The Starting Five
A basketball coach has 12 players on the team. How many ways can he select
Logic Lab Exit Ticket EXIT TICKET: CREATION STATION
Name:
Date:
Logic Lab
1. Original Permutation Scenario
Write a word problem where the order matters . Then, define your \(n\) and \(r\).
\(n = \) ________
\(r = \) ________
Solution: ____________
2. Original Combination Scenario
Write a word problem where you are selecting a group (order does NOT matter).
\(n = \) ________
\(r = \) ________
Solution: ____________
EXIT TICKET: CREATION STATION
(Second copy for easy printing)
Logic Lab Answer Key TEACHER ANSWER KEY
Logic Lab: Scenario Sort Activity
Permutation Pile (Order Matters)
Card Scenario Setup (\(nPr\)) Answer 01 Student Council (Pres, VP, Sec) \(15P3\) 2,730 03 Ranking 3 Movies (out of 10) \(10P3\) 720 05 Arranging 5 Books \(5P5\) (or \(5!\)) 120 07 4-digit Code (No repeats) \(10P4\) 5,040 09 6 Chores to 6 Roommates \(6P6\) (or \(6!\)) 720
Combination Pile (Order Doesn't Matter)
Card Scenario Setup (\(nCr\)) Answer 02 Budget Committee (3 out of 15) \(15C3\) 455 04 2 Pizza Toppings (out of 8) \(8C2\) 28 06 5 Fruit Smoothie (out of 10) \(10C5\) 252 08 4-card Hand (out of 52) \(52C4\) 270,725 10 5 Starters (out of 12) \(12C5\) 792
Teaching Notes & Troubleshooting
The Committee vs. Cabinet Trap: Students often see "people" and assume combination. Remind them that if the people have specific titles (President, VP), it's a permutation.
Calculator Errors: Most common error is putting \(r\) before \(n\). Total items (\(n\)) must always come first in the calculator string.
Wait, Card 09? Card 09 is a permutation because each chore is different. Assigning Chore A to Bob and Chore B to Alice is different than Chore B to Bob and Chore A to Alice.
Exit Ticket Grading: Look for realistic scenarios. If a student writes about a race (P) or a pizza (C), they are on the right track!
