How many ten-digit numbers have at least two equal digits?
1 answer:
Answer:
8,996,734,079 numbers
Step-by-step explanation:
First let's find the number of ten-digit numbers.
The maximum ten-digit number is 9,999,999,999 and the minimum is 1,000,000,000. So the number of ten-digit numbers is:
Now, to find the number of ten-digit numbers with at least two equal digits, we can find the number of ten-digit numbers with all digits different, and then subtract this amount from the total ten-digit numbers.
To find the number of ten-digit numbers with all digits different, we can use the following logic:
The first digit can have 9 different values (0 not included), the second can also have 9 (one digit used), then the third can have 8 (two digits used), the fourth can have 7, and so on. So we have that:
Then the number of ten-digit numbers with at least two equal digits is:
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Answer:
Step-by-step explanation:
To evaluate or simplify expressions with exponents, we use exponent rules.
1. An exponent is only a short cut for multiplication. It simplifies how we write the expression.
2. When we multiply terms with the same bases, we add exponents.
3. When we divide terms with the same bases, we subtract exponents.
4. When we have a base to the exponent of 0, it is 1.
5. A negative exponent creates a fraction.
6. When we raise an exponent to an exponent, we multiply exponents.
7. When we have exponents with parenthesis, we apply it to everything in the parenthesis.
We will use these rules 2 and 7 to simplify. First apply the 4 exponent to both -6 and p. Then add the exponent of the base -6 and p on the outside of the parenthesis.