Mary says that the greater the number of counters, the greater the number of different arrays you can form. Give an example that shows that Mary is wrong.
any prime number allows only one array.
To determine if Mary's statement is accurate or not, we can examine the concept of arrays and counters. An array is a way to organize items in a specific order, while counters are objects used for counting and manipulating quantities.
In this case, Mary claims that increasing the number of counters will result in a greater number of different arrays. To test this statement, let's consider a scenario with three counters: A, B, and C.
By using these three counters, we can form different arrays by changing the counter's position. Let's examine the possible arrays we can form:
1. Array 1: ABC
2. Array 2: BAC
3. Array 3: CAB
4. Array 4: ACB
5. Array 5: BCA
6. Array 6: CBA
As we can observe, using three counters, we are able to create six different arrays.
Now, let's consider a scenario with four counters: A, B, C, and D.
Using these four counters, we can form arrays by changing their positions. Let's explore the possible arrays:
1. Array 1: ABCD
2. Array 2: BCDA
3. Array 3: CDAB
4. Array 4: DABC
5. Array 5: ABDC
6. Array 6: BCAD
7. Array 7: CADB
8. Array 8: DBCA
9. Array 9: ACDB
10. Array 10: BDAC
11. Array 11: CDBA
12. Array 12: DACB
As we can see, with four counters, we are able to create twelve different arrays.
Comparing the number of arrays we can form with three counters (6 arrays) and four counters (12 arrays), it is clear that Mary's statement is incorrect. The greater number of counters does not necessarily result in a greater number of different arrays. In this case, doubling the number of counters only increased the number of arrays by two times, not four times, as Mary suggested.