Photo AI
'n Maatskappy gebruik 'n koderingstelsel om sy kliente te identifiseer - NSC Mathematics - Question 11 - 2017 - Paper 1
Question 11
'n Maatskappy gebruik 'n koderingstelsel om sy kliente te identifiseer. Elke kode bestaan uit twee letters en 'n ry syfers, byvoorbeeld AD108 of RR 45789. Die lette... show full transcript
Worked Solution & Example Answer:'n Maatskappy gebruik 'n koderingstelsel om sy kliente te identifiseer - NSC Mathematics - Question 11 - 2017 - Paper 1
Step 1
Hoeveel verskillende kliente kan geidentifiseer word met 'n koderingstelsel wat uit TWEE letters en TWEE syfers bestaan?
Answer
To calculate the total number of unique identifiers, we first determine the number of choices for the letters and digits:
- The letters can be chosen from A, D, R, S, and U: 5 choices.
- For the first letter, we have 5 possibilities, and for the second letter, we again have 5 possibilities since letters can repeat.
- The digits can be chosen from 0 to 9. Since no digit can repeat, we have 10 possibilities for the first digit and 9 possibilities for the second digit.
The total number of unique codes can be calculated as:
Thus, the total number of unique clients that can be identified is 2250.
Step 2
Bepaal die kleinste getal syfers wat 'n maatskappy nodig het om 700 000 kliente op unieke wyse met hul koderingstelsel te identifiseer.
Answer
To find the smallest number of digits needed to identify at least 700,000 clients with a coding system that includes 2 letters and a varying number of digits, we follow this approach:
- Start with 2 letters:
- Number of combinations = .
- Calculate the total combinations as more digits are included:
- For 1 digit: (not sufficient).
- For 2 digits: (not sufficient).
- For 3 digits: (not sufficient).
- For 4 digits: (not sufficient).
- For 5 digits: (sufficient).
Thus, the smallest number of digits required is 5 to ensure all 700,000 clients can be identified uniquely.