2×3×3×3=54, is this correct sir? I am confused since 51 is the key answerMarkFL said:What have you tried, and where are you stuck?
Thank you sirMarkFL said:The first digit is either 3 or 4. So, let's consider each case separately:
(1) First digit is 3:
Then the rest of the numbers must come from the list: 2, 2, 3, 3, 4, 4, 4, 4
Therefore we may choose any 3-digit sequence except 222 and 333 for the rest of the digits. This shows there are:
\(\displaystyle N_1=3^3-2=25\)
numbers in this case.
(2) First digit is 4:
Then the rest of the numbers must come from the list 2, 2, 3, 3, 3, 4, 4, 4
Therefore we may choose any 3-digit sequence except 222 for the rest of the digits. This shows there are:
\(\displaystyle N_2=3^3-1=26\)
numbers in this case.
Hence, the total number is:
\(\displaystyle N=N_1+N_2=51\)
The formula for finding the number of ways to form 4-digit numbers greater than 3000 is (10 x 10 x 10 x 10) - (3 x 10 x 10 x 10) = 9,000.
Let's say we want to find the number of ways to form 4-digit numbers greater than 3000 using the digits 0, 1, 2, and 3. We would plug in the values into the formula: (4 x 4 x 4 x 4) - (1 x 4 x 4 x 4) = 240 ways.
Yes, the formula can be used for numbers with more or less than 4 digits. The only thing that would change is the number of digits used in the formula. For example, for 3-digit numbers greater than 300, the formula would be (10 x 10 x 10) - (3 x 10 x 10) = 900 ways.
Yes, there are restrictions on the digits that can be used. For this formula, the first digit must be greater than 3 in order for the number to be greater than 3000. Additionally, each digit can only be used once in the number, so there can't be any repeated digits.
No, this formula is specifically for finding the number of ways to form 4-digit numbers greater than 3000 using whole numbers. It cannot be applied to decimals or negative numbers.