Question

How many 5-digit sequences can we form from the integers 1, 2, ..., 9 if:

Answer 1

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

$9\times 9\times 9\times 9\times 9\\\\=9^5\\\\=59049$

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":

$^9P_5=15120$

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":

$^9C_5=126$

Hence, a) 59049, b) 15120, c) 126.