A coded message from a CIA operative to his Russian KGB counterpart is to be sent in the form Q4ET, where the first and last entries must be consonants; the second, an integer 1 through 9; and the third, one of the six vowels. How many different ciphers can be transmitted?

Question

Mathematics

Fiona Olsen

20 October, 18:43

A coded message from a CIA operative to his Russian KGB counterpart is to be sent in the form Q4ET, where the first and last entries must be consonants; the second, an integer 1 through 9; and the third, one of the six vowels. How many different ciphers can be transmitted?

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Answers (1)

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Seth Brady · Answer 1

21,600

Step-by-step explanation:

If in the coding system being used there are 6 vowels (A, E, I, O, U and Y)

Number of Consonants = 26-6 = 20

First entry must be a consonant, therefore the first entry can be chosen in 20 ways. The second entry must be an integer 1 through 9, therefore the second entry can be chosen in 9 ways. The third entry must be one of the six vowels, therefore the third entry can be chosen in 6 ways. The last entry must be a consonant, therefore the last entry can be chosen in 20 ways.

Therefore:

Number of different possible ciphers = 20*9*6*20

=21600