How many number plates can be made if the number plates have two letters of the english alphabet (a-z) followed by two digits (0-9) if the repetition of digits or alphabets is not allowed?
Answers
Answer:
58,500 number plates can be made with 2-letters of English alphabet(a-z) followed by two digits (0-9) without any repetitions of alphabets or digits.
Step-by-step explanation:
We are asked to find out the no. of combinations of number plates we can get with two letters of English Alphabets(A-Z) followed by two digits from 0-9 without any repetition of digits or alphabets.
No of English alphabets (A-Z) = 26
No. of digits (0-9) = 10
We have total four place to cover with two alphabets and two digits.
_ _ _ _
(alphabet) (alphabet) (digit) (digit)
For the first place:
Out of 26 alphabets we need one
∴ combinations for first place = 26C1 = 26! / (26-1)! = (26 * 25!) / 25! = 26
For the second place:
We are left with 25 alphabets now as no repetitions are allowed.
∴combinations for second place= 25C1 = (25 * 24!) / 24! = 25
For the third place:
Out of 10 digits we need to select one
∴combinations for third place = 10C1 = (10 * 9!) / 9! = 10
For the fourth place:
We are left with 9 digits now as no repetitions are allowed
∴combinations for fourth place= 9C1 = (9 * 8!) / 8! = 9
In order to find the total no. of possible number plate that can be made, we will multiply the combinations for each of the places.
∴Total Combinations of number plates = 26 * 25 * 10 * 9 = 58,500