EXERCISES Exercises 1-11. (License Plates) How many different license plates con

Question

EXERCISES Exercises 1-11. (License Plates) How many different license plates consisting of two letten lowed by four digits are possible if: ers fo l. 1. The two letters are different, and the four digits are all the same? 2. 3. 4. same, and the four digits are all odd? The two letters are the The letter A appears first? The letter A appears last? The letter A appears exactly one time? The letter A appears? All of the digits are greater than 5, and the two letters are different? 6. 8. The two letters are different and the first digit is a 0? 9 The two letters are the same and the last digit is a 0? 10.) The two letters are the same, ll he numbers are different, and the last digit is a o? 11. The last digit is a four, and the digits increase as you read from left to right?

Explanation / Answer

here we are considering that letter are not case sensitive therfore 26 choice for letter and 10 choice for digits.

2)

as two letters are same therefore for one letter we have 26 choice and 2nd letter we have one choice which needs to be same as first letter and for each of digits we have 5 choices of odd numbers (1,3,5,7,9)

hence choices =26*1*5*5*5*5 =16250

6) plates of total choices =26*26*10*10*10*10 =6760000

for numebr of plates without A =N( only 25 choices for letters) =25*25*10*10*10*10=6250000

hence plates with letter A =6760000-6250000=510000

10)

for as two letters are same therefore for one letter we have 26 choice and 2nd letter we have one choice which needs to be same as first letter ; for first digit 9 choice except 0; second digit remaining 8 ; third digit 7 and for fourth digit 1 choice which is 0.

hence total number plates =26*1*9*8*7*1=13104

( please revert for any clarification)

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