How many numbers greater than 1000000 can be formed by using the digits 1, 2, 0, 2, 4, 2, 4?

Step 1: Analyze the given digits and number of places

We are given seven digits: 1, 2, 0, 2, 4, 2, 4. We need to form numbers greater than 1,000,000 using all these digits. A number greater than 1,000,000 must have at least 7 digits. Since we have exactly 7 digits, we must form 7-digit numbers.

Step 2: Calculate total permutations of the digits

First, let's find the total number of distinct 7-digit numbers that can be formed using these digits. We have 7 digits in total, with the digit '2' repeating 3 times and the digit '4' repeating 2 times. The formula for permutations with repetitions is $n! / (n_1! n_2! ...)$, where $n$ is the total number of digits and $n_i$ is the frequency of each repeating digit.

Step 3: Calculate permutations where '0' is the first digit

A 7-digit number cannot start with '0'. If '0' is placed in the first position, the number becomes a 6-digit number, which is not greater than 1,000,000. So, we need to subtract these invalid numbers from the total permutations. If '0' is fixed at the first position, we are left with 6 digits: 1, 2, 2, 2, 4, 4. The digit '2' repeats 3 times and '4' repeats 2 times.

Step 4: Subtract invalid permutations from total permutations

To find the number of 7-digit numbers greater than 1,000,000, we subtract the numbers that start with '0' (which are effectively 6-digit numbers) from the total number of permutations of the given digits.

More from this chapter

• Find the probability that in a random arrangement of the letters of the word MATHEMATICS, the two A's are not together.
• 36. Find the number of ways in which six people can ride a toboggan if one of a subset of three must drive. 37. (a) Find the number of ways in which five person
• In how many ways can 4 red, 3 yellow and 2 green discs be arranged in a row if the discs of the same colour are indistinguishable?
• How many numbers lying between 100 and 1000 can be formed with the digits 0, 1, 2, 3, 4, 5, if the repetition of the digits is not allowed?
• How many ways can a 2×n rectangle be tiled using 1×2 dominoes?
• The largest n N such that 3^n divides 50! is:
• How many 4-digit numbers can be formed by using the digits 1 to 9 if repetition of digits is not allowed?
• The number of 3-digit numbers, that are divisible by 2 and 3, but not divisible by 4 and 9, is

All Permutations and Combinations solutions →