Respuesta :
Answer:
(a) The no. of 3 elements list is [tex]n^{2}[/tex]
(b) The no. of 3 elements list is [tex]n^{3} - n^{2}[/tex]
Step-by-step explanation:
As per the question:
Total no. of possible elements = n
The no. of elements required out of n elements to form the list = 3
Now,
(a) When the first and last entries on the list are same:
No. of ways for the entry of first element = n ways
No. of ways for the entry of second element when it can be entered without any restriction = n ways
No. of ways for the entry of last element as it has to be the same as the first element = 1 way
Thus the total no. of 3 elements list according to the multiplication principle:
[tex]n\times n\times 1 = n^{2}[/tex]
(b) When the first and the last entries must be distinct:
No. of ways for the entry of first element = n ways
No. of ways for the entry of second element when it can be entered without any restriction = n ways
No. of ways for the entry of last element as it has to be different from the first element = (n - 1) ways
Thus the total no. of 3 elements list according to the multiplication principle:
[tex]n\times n\times (n - 1) = n^{2}(n - 1)\ ways = n^{3} - n^{2}[/tex]
