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How many car number plates can be made if
i) each plate contains 2 different letters of English alphabet, followed by 3 different digits.
ii) the number plates have two letters of the english alphabet followed by two digits if the repetition of digits or alphabets is not allowed?
- a)i) 468000 ; ii) 58500
- b)i) 542000 ; ii) 58500
- c)i) 58500 ; ii) 468000
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
How many car number plates can be made ifi) each plate contains 2 diff...
i) There are 5 places to fill
2 places of alphabet(out of 26) can be filled in =26∗25 ways
3 places of digits(out of 10) can be filled in = 10∗9∗8 ways
No of different plates = 26∗25∗10∗9∗8=468000
ii) We have total four place to cover with two alphabets and two digits.
For the first place:
Out of 26 alphabets we need one
∴ combinations for first place = 26C1 = 26
For the second place:
We are left with 25 alphabets now as no repetitions are allowed.
∴combinations for second place= 25C1 = 25
For the third place:
Out of 10 digits we need to select one
∴combinations for third place = 10C1 = 10
For the fourth place:
We are left with 9 digits now as no repetitions are allowed
∴combinations for fourth place= 9C1 = 9
∴Total Combinations of number plates = 26 * 25 * 10 * 9 = 58,500
Most Upvoted Answer
How many car number plates can be made ifi) each plate contains 2 diff...
To calculate the number of car number plates that can be made, we need to consider the given conditions.
i) Each plate contains 2 different letters of the English alphabet, followed by 3 different digits.
To solve this, we need to consider the number of choices available for each character on the number plate.
- For the first letter: There are 26 choices available (as there are 26 letters in the English alphabet).
- For the second letter: Since repetition is not allowed, there are 25 choices available (after using one letter for the first position).
- For the first digit: There are 10 choices available (from 0 to 9).
- For the second digit: Since repetition is not allowed, there are 9 choices available (after using one digit for the first position).
- For the third digit: Since repetition is not allowed, there are 8 choices available (after using two digits for the first and second positions).
Now, we can calculate the total number of car number plates by multiplying the number of choices available for each character:
Total number of car number plates = 26 * 25 * 10 * 9 * 8 = 468,000
Therefore, the correct answer for part i) is 468,000.
ii) The number plates have two letters of the English alphabet followed by two digits.
Similarly, we need to consider the number of choices available for each character on the number plate.
- For the first letter: There are 26 choices available.
- For the second letter: Since repetition is not allowed, there are 25 choices available (after using one letter for the first position).
- For the first digit: There are 10 choices available.
- For the second digit: Since repetition is not allowed, there are 9 choices available (after using one digit for the first position).
Total number of car number plates = 26 * 25 * 10 * 9 = 58,500
Therefore, the correct answer for part ii) is 58,500.
Hence, the correct answer is option A (468,000 for part i) and 58,500 for part ii)).
i) Each plate contains 2 different letters of the English alphabet, followed by 3 different digits.
To solve this, we need to consider the number of choices available for each character on the number plate.
- For the first letter: There are 26 choices available (as there are 26 letters in the English alphabet).
- For the second letter: Since repetition is not allowed, there are 25 choices available (after using one letter for the first position).
- For the first digit: There are 10 choices available (from 0 to 9).
- For the second digit: Since repetition is not allowed, there are 9 choices available (after using one digit for the first position).
- For the third digit: Since repetition is not allowed, there are 8 choices available (after using two digits for the first and second positions).
Now, we can calculate the total number of car number plates by multiplying the number of choices available for each character:
Total number of car number plates = 26 * 25 * 10 * 9 * 8 = 468,000
Therefore, the correct answer for part i) is 468,000.
ii) The number plates have two letters of the English alphabet followed by two digits.
Similarly, we need to consider the number of choices available for each character on the number plate.
- For the first letter: There are 26 choices available.
- For the second letter: Since repetition is not allowed, there are 25 choices available (after using one letter for the first position).
- For the first digit: There are 10 choices available.
- For the second digit: Since repetition is not allowed, there are 9 choices available (after using one digit for the first position).
Total number of car number plates = 26 * 25 * 10 * 9 = 58,500
Therefore, the correct answer for part ii) is 58,500.
Hence, the correct answer is option A (468,000 for part i) and 58,500 for part ii)).
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How many car number plates can be made ifi) each plate contains 2 different letters of English alphabet, followed by 3 different digits.ii)the number plates have two letters of the english alphabetfollowed by two digitsif the repetition of digits or alphabets is not allowed?a)i) 468000 ; ii) 58500b)i) 542000 ; ii) 58500c)i) 58500 ; ii) 468000d)None of theseCorrect answer is option 'A'. Can you explain this answer?
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