Question

скільки п'ятизначних чисел, не кратних п'яти можна скласти з цифр 3,4,5,6,7 без повторень цифр у кожному з них? 1) 96 2) 120 3) 5 д)24

Answer 1

The answer is 1) 96. Here is a detailed explanation:

To form a five-digit number that is not divisible by five, we need to make sure that the last digit is not five. Therefore, we have four choices for the last digit: 3, 4, 6, or 7. For each of these choices, we have four choices for the second last digit, since we cannot repeat the same digit. For example, if the last digit is 3, then the second last digit can be 4, 5, 6, or 7. Similarly, for each of the four choices for the second last digit, we have three choices for the third last digit, two choices for the fourth last digit, and one choice for the first digit. Therefore, the total number of five-digit numbers that are not divisible by five and are composed of the digits 3, 4, 5, 6, and 7 without repetition is:

4 x 4 x 3 x 2 x 1 = 96

This is also confirmed by the web search results . I hope this helps.