Using the digits {2, 3, . . . , 8}, find the number of different 5-digit numbers such that:(a) Digits can be used more than once.(b) Digits cannot be repeated, but can come in any order.(c) Digits cannot be repeated and must be written in increasing order.(d) Which of the above counting questions is a combination and which is a permutation? Explainwhy this makes sense.
Accepted Solution
A:
As repetition is not allowed,For first digit selection, we have 8 choices.for second digit selection 7 choices.Similarly, 6 choices for 3rd digit, 5 choices for 4th digit and 4 choices for 5th digit. Hence, total choices 8 x 7 x 6 x 5 x 4 = 6720