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Numbers of four different digits are formed by using the digits 1, 2, 3, 4, 5, 6 and 7 in all possible ways without repetition. How many of them are greater than 3400?
- a)840
- b)560
- c)480
- d)120
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Numbers of four different digits are formed by using the digits 1, 2,...
Number of numbers greater than 3000 = 5 × 6 × 5 × 4 = 600
Number of numbers between 3000 and 3400 = 1 × 2 × 5 × 4 = 40
So, number of numbers greater than 3400 are 560.
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Community Answer
Numbers of four different digits are formed by using the digits 1, 2,...
To find the numbers greater than 3400, we need to consider the thousands place digit. The thousands place digit can only be 4, 5, 6, or 7, as numbers less than 3400 will have a thousands place digit of 1, 2, or 3.
To solve this problem, we can break it down into the following steps:
1. Determine the number of possible digits for each place value:
- Thousands place: 4 options (4, 5, 6, 7)
- Hundreds place: 6 options (any digit except the one already used for the thousands place)
- Tens place: 5 options (any digit except the two already used for the thousands and hundreds place)
- Units place: 4 options (any digit except the three already used for the thousands, hundreds, and tens place)
2. Calculate the number of possible numbers greater than 3400:
- For each option in the thousands place, there are 6 options for the hundreds place, 5 options for the tens place, and 4 options for the units place.
- Therefore, the total number of possible numbers is 4 * 6 * 5 * 4 = 480.
Hence, the correct answer is option C) 480.
To solve this problem, we can break it down into the following steps:
1. Determine the number of possible digits for each place value:
- Thousands place: 4 options (4, 5, 6, 7)
- Hundreds place: 6 options (any digit except the one already used for the thousands place)
- Tens place: 5 options (any digit except the two already used for the thousands and hundreds place)
- Units place: 4 options (any digit except the three already used for the thousands, hundreds, and tens place)
2. Calculate the number of possible numbers greater than 3400:
- For each option in the thousands place, there are 6 options for the hundreds place, 5 options for the tens place, and 4 options for the units place.
- Therefore, the total number of possible numbers is 4 * 6 * 5 * 4 = 480.
Hence, the correct answer is option C) 480.
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