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The number plate of a car can have 3 letters followed by 4 digits and
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29 Oct 2024, 01:19
29 Oct 2024, 01:19
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Question Stats:
58% (01:19) correct
41% (01:53) wrong based on 12 sessions
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The number plate of a car can have 3 letters followed by 4 digits and repetition of both letters and digits can occur in the number plate. If the letters that can be used are A, F and G and numbers that can be used are 1, 2 and 3, then in how many different ways can the number plate be made?
A. \(7!\)
B. \(3! x 4!\)
C. \(3^5\)
D. \(3^7\)
E. \(7^3\)
A. \(7!\)
B. \(3! x 4!\)
C. \(3^5\)
D. \(3^7\)
E. \(7^3\)
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Re: The number plate of a car can have 3 letters followed by 4 digits and
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29 Oct 2024, 08:54
29 Oct 2024, 08:54
1
To determine the number of different ways to create a number plate consisting of 3 letters followed by 4 digits, with repetition allowed:
Letters: We can use A, F, and G. This gives us 3 choices for each of the 3 letter positions. So, the total combinations for the letters is
3×3×3=3
Digits: We can use 1, 2, and 3. Similarly, this gives us 3 choices for each of the 4 digit positions. So, the total combinations for the digits is
3×3×3×3=3
Now, we combine the two results:
Total combinations = 3^7
Letters: We can use A, F, and G. This gives us 3 choices for each of the 3 letter positions. So, the total combinations for the letters is
3×3×3=3
Digits: We can use 1, 2, and 3. Similarly, this gives us 3 choices for each of the 4 digit positions. So, the total combinations for the digits is
3×3×3×3=3
Now, we combine the two results:
Total combinations = 3^7
gmatclubot
Re: The number plate of a car can have 3 letters followed by 4 digits and [#permalink]
29 Oct 2024, 08:54
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