The image you provided contains a mathematical problem written in Japanese. Here is a translation and interpretation of the problem:

Problem:

"次の質問に答えよ。
5個の数字1, 2, 3, 4, 5を使ってできる5桁の整列の整数について、次の問いに答えなさい。ただし、同じ数字は何度も使わないこととする。

1. 5桁の整数の総数は何個ですか？
2. 5が1の位の数である5桁の整数は何個ですか？"

Translation:

"Answer the following questions.
Regarding the 5-digit integers that can be formed using the digits 1, 2, 3, 4, and 5, answer the following questions. Note that the same digit cannot be used more than once.

1. How many total 5-digit integers can be formed?
2. How many 5-digit integers have 5 as the unit's (ones) digit?"

Solution:

1. Total Number of 5-Digit Integers:

   • Since the problem states that we cannot repeat digits, the number of different 5-digit integers that can be formed is calculated by the factorial of 5.
   • $5! = 5 \times 4 \times 3 \times 2 \times 1 = 120$
   • Therefore, the total number of 5-digit integers that can be formed is 120.

2. 5-Digit Integers with 5 as the Unit Digit:

   • If 5 is fixed as the unit digit, then we need to arrange the remaining 4 digits (1, 2, 3, 4) in the other four positions.
   • The number of different 4-digit numbers that can be formed with 4 digits is $4! = 4 \times 3 \times 2 \times 1 = 24$.
   • Therefore, the number of 5-digit integers with 5 as the unit digit is 24.

Would you like more details or have any questions?

Related Questions:

1. How many 5-digit numbers can be formed if repetition of digits is allowed?
2. What is the probability that a randomly chosen 5-digit number has 5 as the unit digit?
3. How many 4-digit numbers can be formed using the digits 1, 2, 3, and 4 without repetition?
4. If the digits were to be arranged in descending order, how many such 5-digit numbers would exist?
5. How many 5-digit numbers are divisible by 2?

Tip:

When solving problems involving permutations, remember to carefully consider whether digits can be repeated, as this significantly impacts the total number of possibilities.