How many license plates can be made using either two uppercase English letters followed by four digits or two digits followed by four uppercase English letters?
35,152,000 (assuming that 000 is a valid number, and that no letter combinations are disallowed for offensive connotations.) Also, no letters are disallowed because of possible confusion between letters and numbers eg 0 and O.
it 26 to the power 4 and then 99 for the numbers figure that out add the two together
It is possible to create a 3-digit number, without repeated digits so the probability is 1.
2600
How many license plates can be made using either two uppercase English letters followed by four digits or two digits followed by four uppercase English letters?
There are up to 3 numbers and up to 5 letters in a UK postcode. One or two letters, followed by one or two digits OR one digit and a letter, followed by a space, followed by one digit, followed by two letters.
35,152,000 (assuming that 000 is a valid number, and that no letter combinations are disallowed for offensive connotations.) Also, no letters are disallowed because of possible confusion between letters and numbers eg 0 and O.
3!*3!=36For example, if you want to use the alphabets a,b,c and three digits 1,2,3 you can make the following 36 different passwords (3 letters followed by 3 digits)abc123abc132abc231abc213abc312abc321acb123acb132acb231acb213acb312acb321bca123bca132bca231bca213bca312bca321bac123bac132bac231bac213bac312bac321cab123cab132cab231cab213cab312cab321cba123cba132cab231cab213cab312cab321
Independent events, so P(both)=(5/26)(4/10)=0.07692307692. The 4/10 comes from the fact that 0, 3, 6, and 9 are the 4 digits that are multiples of 3.
None of the digits can be 10, so the probability is 0.
(26) x (26) x (10,000) = 6,760,000
There are 26 different letters that can be chosen for each letter. There are 10 different numbers that can be chosen for each number. Since each of the numbers/digits that can be chosen for each of the six "spots" are independent events, we can multiply these combinations using the multiplicative rule of probability.combinations = (# of different digits) * (# of different digits) * (# of different digits) * (# of different letters) * (# of different letters) * (# of different letters) = 10 * 10 * 10 * 26 * 26 * 26 = 103 * 263 = 1000 * 17576 = 17,576,000 different combinations.
If all letters and numbers are allowed, the possibilities are 26x26x10x10x10x10. So: 6760000 different plates.
It was digits followed by zero
There are ten digits and twenty-six letters, assuming unconstrained choice of both. The probability of getting a repetition in the first two digits is 10/100, since there are 10 repetitious combinations of two digits among the 100 pairs of digits possible.To calculate the probability of a repetition in the two letters, consider that there are 262 combinations, of which 26 X 25 do not contain repetitions. (There is free choice among 26 alternatives for the first letter, but only 25 choice for the following letter.) Therefore, the probability of a repetition within the two letters is (26)(25)/262 or 25/26.The chance of a repeated digit within the four digit bloc is (10)(9)(8)(7)/104) or 504/1000.If there is no repetition of a digit within either the two-digit bloc or the four-digit bloc, there is still a chance of repetition of a digit between the blocs. The chance of this is (8 X 7 X 6 x 5)/104 or 168/1000.To reach the final answer, it is advantageous to calculate first the probability of not getting the specified repetition and then subtract this number from one. The probability of not getting a repetition in the first bloc is 9/10, and the probability of not getting a repetition between the first and second blocs is 168/1000. Therefore, the probability of not getting a repetition within the first bloc or between the first and the second number blocs is the product of these two, or 1512/10,000. Further multiplications by the independent probabilities of no repetition within the two remaining blocs yields a value of about 2.88 X 10-4. Therefore, the probability of at least one of the repetitions specified is about 0.999712.
it 26 to the power 4 and then 99 for the numbers figure that out add the two together