Question

imagine a license plate created 3 uppercase letters followed by 3 digits(1-9) The license plate can repeat letters and numbers. How many unique license plates exist? A) 1,2576 B) 7, 862,400 C) 12, 812,904 D) 17, 576,000

Answer 1

Hey dear here is the answer


1 answer · Mathematics 

 Best Answer

There are 26 letters, so there are 26^3 possible 3-letter sequences. 
the number of these which are palindromes can be computed as follows: 

26 choices for the first letter 
26 choices for the second letter 
1 choice for the third letter ( it has to agree with the first) 

number of ways = 26^2 

Probability of a letter palindrome = 26^2 / 26^3 = 1/26 

there are 10 digits, so there are 10^3 sequences of digits. 
Reasoning as above, the number of digit-palindromes is (10)(10)(1) = 10^2 
so the probability of a digit-palindrome is 10^2 / 10^3 = 1/10 

The events 
D :"digit palindrome" 
L: "letter palindrome" 

are independent but not mutually exclusive. 

So, P(L or D) = P(L) + P(D) - P( L and D) 
P(L or D) = P(L) + P(D) - P(L)P(D) 

= 1/26 + 1/10 - (1/26)(1/10) 

= 10/260 + 26/260 - 1/260 
= 35/360 = 7/52




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