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- How many integers can be formed using the prime numbers below 9 that lies between 5000 to 9000, where 1st two digits are same as next two digits.Option: 1</stron
How many integers can be formed using the prime numbers below 9 that lies between 5000 to 9000, where 1st two digits are same as next two digits.
15
18
16
10
Answers (1)
To find the number of integers that can be formed using the prime numbers below 9 (2, 3, 5, and 7) where the first two digits are the same as the next two digits to form a 4-digit number between 5000 and 9000, we can consider the following cases:
Case 1: The first two digits are 22
In this case, we only have one choice for the first two digits (22). For the next two digits, we have 4 choices (2, 3, 5, and 7). So, the total number of integers in this case is:
Case 3: The first two digits are 55In this case, we only have one choice for the first two digits (55). For the next two digits, we have 4 choices (2, 3, 7 since 5 is already used). So, the total number of integers in this case is:
Case 4: The first two digits are 77
In this case, we only have one choice for the first two digits (77). For the next two digits, we have 4 choices (2, 3, 5 since 7 is already used). So, the total number of integers in this case is:
Adding up the four cases, we get:
Therefore, the number of integers that can be formed using the prime numbers below 9 (2, 3, 5, and 7) where the first two digits are the same as the next two digits to form a 4-digit number between 5000 and 9000 is 16.
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