Table of Contents
- 1 How many 3 digit numbers contain the number 7?
- 2 How many 3 digit numbers contain the digit 7 at least once?
- 3 How many 3-digit numbers have at least one 6 and 7?
- 4 How many three digit numbers have 7 exactly once in them?
- 5 How many possible values can a three digit number accept?
- 6 How many ways can the unit place be filled in numbers?
How many 3 digit numbers contain the number 7?
So, with 7 in the unit place, the 3 digited number can be formed in 8 x 9 = 72 ways. Hence, with 7 occurring exactly once, there are 81 + 72 + 72 = 225 three digited numbers.
How many 3 digit numbers contain the digit 7 at least once?
There are 450 even numbers with three digits. If there is no seven the hundreds digit is one of eight (no zero or seven), and the tens digit is one of nine (no seven). So 8×9×5 with no seven – that is 360 leaving 90 with a seven.
How many 3 digit numbers have at least one of their digits as 5?
So the total is 9*18+81. Total three digit numbers having one or more 5 are 72+72+81=225 numbers.
How many 3-digit numbers have at least one 6 and 7?
The answer is that there are 52 three-digit integers that have both a 6 & 7 digit.
How many three digit numbers have 7 exactly once in them?
There are 900 three digit numbers and out of 900 numbers there are 225 numbers having 7 exactly once. Thus, 225 is the required answer. There are Hundredth place, Tenth place and Unit place in a 3 digited number. Put 7 in hundredth position.
How many digited numbers can be formed in 9 x 8?
Hence, with 7 in the tenth place, the 3 digited numbers can be formed in 9 x 8 = 72 ways. Lastly, putting 7 in the unit place, the hundredth place can be formed in 8 ways (as 0 and 7 cannot be put here) and for each of these 8 ways, the tenth place can be formed in 9 ways.
How many possible values can a three digit number accept?
Here the number of three number is (999-100)+1=900. Now, if no digit is 3, then the highest digits can be one of 0 to 9 excluding 0,3 as 0 will reduce the number to 2-digit. So, the highest can accept 8 possible values. The rest two digits each can accept one of 0 to 9 excluding 3.
How many ways can the unit place be filled in numbers?
There are Hundredth place, Tenth place and Unit place in a 3 digited number. Put 7 in hundredth position. Then tenth place can be filled in 9 ways (since out of 10 digits 0,1,2,……9 the digit 7 occupying hundredth place is excluded). Again for ieach of these 9 ways, the unit place can be filled in 9 ways.