In the past, a local telephone number in a country consisted of a sequence of three letters followed

Regina Ewing

Regina Ewing

Answered question

2022-04-10

In the past, a local telephone number in a country consisted of a sequence of three letters followed by four digits. Three letters were associated with each number from 2 to 9 (just as in the standard telephone layout shown in the figure) so that each telephone number corresponded to a sequence of seven digits. How many different sequences of seven digits were possible?

Answer & Explanation

Blaine Andrews

Blaine Andrews

Beginner2022-04-11Added 20 answers

There are 24 letter
Thus, the number of arrangements possible for three 3 letters out o 24 letters are
24 P 3 = 24 ! ( 24 3 ) !
= 24 ! 21 !
= 24 × 23 × 22
= 12 , 144

And the number of arrangements from 10 digit numerals taken 4 at a time
12 P 4 = 12 ! ( 12 4 ) !
= 12 ! 8 !
= 12 × 11 × 10 × 9
= 11 , 880

So the Total number of possible sequences would be 1 , 44 , 270 , 720

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