Gegee die syfers: 3; 4; 5; 6; 7; 8 en 9 11.1 Bereken hoeveel unieke 5-syfer-kodes gevorm kan word deur die syfers hierdie te gebruik, indien: 11.1.1 Die syfers herhaal kan word 11.1.2 Die syfers nie herhaal kan word nie 11.2 Hoeveel unieke 3-syfer-kodes kan gevorm word deur die syfers hierdie te gebruik, indien: Sifers herhaal kan word Die kode groter as 400 maar kleiner as 600 is Die kode deur 5 deelbaar is - NSC Mathematics - Question 11 - 2018 - Paper 1

For this part, we need to select 5 digits from the 7 available, and the order matters since each position must be filled with a different digit. The number of arrangements can be calculated as:

$7 imes 6 imes 5 imes 4 imes 3 = 2520$

To calculate the number of 3-digit codes where digits can be repeated, we have 7 options for each of the three positions:

$7^3 = 343$

For 3-digit codes between 400 and 600, the first digit must be 4 or 5. There are 2 choices for the first digit, and since the digits can be repeated, there are 7 choices for the second digit and 7 for the third:

$2 imes 7 imes 7 = 98$

For a 3-digit number to be divisible by 5, the last digit must be either 0 or 5. Therefore, we can have the last digit as one of 2 options (0 or 5), and for each of the first two digits, we can select any of the 7 digits, thus:

$7 imes 7 imes 2 = 98$