A MOPED LICENCE PLATE HAS TWO LETTERS AND THEN FOUR NUMBERS IN IT HOW MANY PLATES CAN BE MADE WITHOUT DUPLICATING THERE ARE NO PLATES WITH NUMBER ZERO
Answers
67,59,324 number plates can be made
Step-by-step explanation:
LICENCE PLATE HAS TWO LETTERS AND THEN FOUR NUMBERS IN IT
NO PLATES WITH NUMBER ZERO ( Means no 0000)
As license plate has format
LL NNNN
so we will not do the arrangements of these
LL can be 26 * 26
NNNN - 10 * 10 * 10 * 10
Total cases = 26 * 26 * 10 * 10 * 10 * 10
But this includes
LL0000 case
Hence 26 * 26 Cases to be decrease
Number of plates = 26 * 26 * 10 * 10 * 10 * 10 - 26 * 26
= 26 * 26(10⁴ - 1)
= 26 * 26 (10000 - 1)
= 26 * 26 * 9999
= 67,59,324
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Answer:
I assume it means no plate can have "xx0000" but it can have "xx0473" or " xx0001" right?
On that asumption, the number of the plate can be formed when ist letter is selected and then2nd and then ist numeric digit , then 2nd, then 3rd and then 4th numeric digit are selected.
Ist letter can be selected in 26 ways, second letter also in 26 ways (as it is not mentioned that alphabets should be different), Ist numeric in 10 ways (i.e. any of the 10 digits), 2nd numeric also 10 ways, 3rd numeric also 10 ways and 4th also 10 ways so total ways will be 26 * 26 * 10*10*10*10 = 6760000 ways. But these include numerics 0000 also which will be 26*26*1 ways = 676 ways (ist letter 26 ways, 2nd letter 26 ways and then 4 digits 0000 in one way so total 26*26*1 ways)
So total no of plates = 6760000 - 676 = 6759524 ways