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How many 2-digit numbers contain the digit?
It would help to know which digit. 0 appears in 9 numbers and each of the others in 18 numbers.
How many 4 digit numbers have 6 as their second digit?
There are 9 digits that can be the first digit (1-9); for each of these there is 1 digit that can be the second digit (6); for each of these there are 10 digits that can be the third digit (0-9); for each of these there are 10 digits that can be the fourth digit (0-9). → number of numbers is 9 × 1 × 10 × 10 = 900 such numbers.
If using numbers 1 through 9 how many different 4 digit combinations can be made with no restrictions on order or repeats?
Each digit can appear in each of the 4 positions. There are 9 digits, therefore there are 9⁴ = 6561 such combinations.
How many different three digit numbers can be written using the digits 1 through 9?
You can select 9 numbers for the first digit, 8 numbers for the second digit, and 7numbers for the third digit; so 504 (e.g. 9*8*7) different three digit numbers can be written using the digits 1 through 9.
How many 7 digit combinations can you have if you can only use the numbers 0 through 9 once each?
10!/3! = 604800 different combinations.
