Answer: a) 59049, b) 15120, c) 126.
Step-by-step explanation:
Since we have given that
5 digit sequences from the integers 1,2,...9.
a) the digits can be the same.
Repetition is allowed.
So, Number of ways to form 5 digit sequences would be
[tex]9\times 9\times 9\times 9\times 9\\\\=9^5\\\\=59049[/tex]
b) the digits cannot be the same and the order in which they appear matters.
Repetition is not allowed and order is maintained, so we will use "Permutation":
[tex]^9P_5=15120[/tex]
c) the digits cannot be the same and the order in which they appear does not matter.
Repetition is not allowed and order is not maintained, so we will use "Combination":
[tex]^9C_5=126[/tex]
Hence, a) 59049, b) 15120, c) 126.
