Any number with 2 numbers in it is a 2. Example: 95 They are numbers 10 - 99.
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By using the 3 digits of a number we can form 3 different two digit numbers. 3C2 = 3!/[(3 - 2)!2!] = 3!/(1!2!) = (3 x 2!)/2! = 3
There are only 999 three digit whole numbers.
2240
There are 9 1-digit numbers and 16-2 digit numbers. So a 5 digit combination is obtained as:Five 1-digit numbers and no 2-digit numbers: 126 combinationsThree 1-digit numbers and one 2-digit number: 1344 combinationsOne 1-digit numbers and two 2-digit numbers: 1080 combinationsThat makes a total of 2550 combinations. This scheme does not differentiate between {13, 24, 5} and {1, 2, 3, 4, 5}. Adjusting for that would complicate the calculation considerably and reduce the number of combinations.
On a number line, the digits from 10 to 99 are all two digit numbers. How many numeber are that? There is a short cut. You can subtract 10 from 99 and that gives you the number of numbers between 10 and 99 including 10, but you need to add one more to include 99 as well. So, 10 from 99 is 89 adding 1 is 90 ,which is the amount of numbers total that are two digit. The probability of guessing a two digit number is 1/90 =D