Counting and probablity addition rule?

  • Context: Undergrad 
  • Thread starter Thread starter Tleeves
  • Start date Start date
  • Tags Tags
    Addition Counting
Click For Summary
SUMMARY

The discussion focuses on calculating the number of distinct numbers that an eight-digit calculator display can show, considering the placement of a decimal point and a minus sign. The initial approach used the multiplication rule, counting choices for each digit, but failed to account for repeated values like 1.9 and 1.90. A more accurate method involves applying the addition rule to handle different lengths of numbers separately, ensuring that repetitions are not counted multiple times.

PREREQUISITES
  • Understanding of basic combinatorial principles, including the multiplication and addition rules.
  • Familiarity with the concept of distinct counting in mathematics.
  • Knowledge of decimal representation and number formatting.
  • Ability to analyze and differentiate between unique and repeated values in numerical sets.
NEXT STEPS
  • Research combinatorial counting techniques in detail.
  • Learn about distinct counting methods in probability theory.
  • Explore examples of applying the addition rule in combinatorial problems.
  • Study the implications of number formatting on counting distinct values.
USEFUL FOR

Mathematicians, educators, students studying probability and combinatorics, and anyone interested in understanding distinct counting methods in numerical displays.

Tleeves
Messages
1
Reaction score
0
A calculator has an eight -digit display and a decimal point that is located at the extreme right of the number displayed, at the extreme left or between any pair of digits. The calculator can also display a minus sign at the etreme left of the number. How many distinct numbers can the calculator display? (not the certain numbers are equal, such as 1.9, 1.90, 01.900, and should, therefore, not be counted twice.)

i have
12 choices for the first digit , 10 for the 2nd, 9 for the 3rd, 8 for the 4th, 7 for the 5th, 6 for the 6th, 5 for the 7th, 4 for the 8th.

But this is using the multiplication rule and doesn't account for the numbers such as 1.9, 1.90, 01.900 which the addition rule would. I can't figure out else to do it and am not sure if I'm supposed to use the addition rule.
 
Physics news on Phys.org
Welcome to PF!

Hi Tleeves! Welcome to PF! :smile:
Tleeves said:
… 12 choices for the first digit , 10 for the 2nd, 9 for the 3rd, 8 for the 4th, 7 for the 5th, 6 for the 6th, 5 for the 7th, 4 for the 8th.

uhh? except for the repetitions, it would be 10 choices for the first digit , 10 for the 2nd, 10 for the 3rd, … 10 for the 8th.

I think you'll need to deal with each "length" separately (where the length of a number would be the length from the first non-zero digit to the last non-zero digit), to avoid double-counting the repetitions.
 

Similar threads

Undergrad Probability of getting 3 heads or more in 20 coin flips
  • · Replies 2 ·
Replies
2
Views
2K
MHB Probability question from TV, cracking a phone password
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Permutation - 7 identical items, 32 distinct containers
  • · Replies 18 ·
Replies
18
Views
5K
Graduate Permutation & Combination of multiple duplicates
  • · Replies 16 ·
Replies
16
Views
10K
Physics Questions by a First Year UofToronto Physics Student on Grad Admissions
  • · Replies 26 ·
Replies
26
Views
5K
How to Visually Document Darts League Playoff Progressions and Results?
  • · Replies 1 ·
Replies
1
Views
2K
Programs Does this look like a fine degree?
  • · Replies 7 ·
Replies
7
Views
3K
Number of combinations of marbles in a bag
  • · Replies 5 ·
Replies
5
Views
7K
Mastering the Multiplication Rule: 1000 to 9999
  • · Replies 4 ·
Replies
4
Views
19K
Acceleration and velocity of cart travelling down an inclined plane.
  • · Replies 4 ·
Replies
4
Views
8K