Question

Сколько двузначных чисел можно составить из цифр 2.7.8 при условии что пункт а. цифры могут повторятся пункт б цифры не могут повторятсярешите срочно

Answer 1

А)22 27 28 77 72 78 88 82 87
Б)27 28 72 78 82 87

Answer 2

Number of Two-Digit Numbers with Repeated Digits

To find the number of two-digit numbers that can be formed using the digits 2, 7, and 8, we need to consider two cases: when the digits can repeat and when they cannot repeat.

# a. Digits Can Repeat

When the digits can repeat, we can choose any of the three digits for each of the two positions in the two-digit number. Therefore, the total number of two-digit numbers that can be formed is calculated by multiplying the number of choices for each position:

Number of choices for each position = 3 (since we have three digits: 2, 7, and 8)

Total number of two-digit numbers = Number of choices for each position ^ Number of positions

Total number of two-digit numbers = 3^2 = 9

Therefore, when the digits can repeat, we can form 9 two-digit numbers using the digits 2, 7, and 8.

# b. Digits Cannot Repeat

When the digits cannot repeat, we need to consider the choices for each position differently. For the first position, we have three choices (2, 7, or 8). After choosing a digit for the first position, we have two remaining digits to choose from for the second position. Therefore, the total number of two-digit numbers that can be formed without repeating digits is calculated by multiplying the number of choices for each position:

Number of choices for the first position = 3 (since we have three digits: 2, 7, and 8) Number of choices for the second position = 2 (since we have two remaining digits after choosing one for the first position)

Total number of two-digit numbers = Number of choices for the first position * Number of choices for the second position

Total number of two-digit numbers = 3 * 2 = 6

Therefore, when the digits cannot repeat, we can form 6 two-digit numbers using the digits 2, 7, and 8.

In summary: - When the digits can repeat, we can form 9 two-digit numbers. - When the digits cannot repeat, we can form 6 two-digit numbers.

I hope this helps! Let me know if you have any further questions.