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You know that the first three numbers of a telephone number are 343, but you have forgotten the last 4 digits. You can only recall that the last 4 digits are 3, 6, 8, and 9, but you do not know the order. What is the maximum number of telephone calls you will need to make in order to dial the correct number?

Respuesta :

Answer:

[tex]24[/tex]

Step-by-step explanation:

GIVEN: The first three numbers of a telephone number are [tex]343[/tex], but you have forgotten the last [tex]4[/tex] digits. You can only recall that the last [tex]4[/tex] digits are [tex]3[/tex], [tex]6[/tex], [tex]8[/tex], and [tex]9[/tex], but you do not know the order.

TO FIND: The maximum number of telephone calls you will need to make in order to dial the correct number.

SOLUTION:

length of telephone number [tex]=7[/tex]

last [tex]4[/tex] digits [tex]=3,6,8,9[/tex]

As we do not know the order of digits, to find out the correct phone numbers we will have to call every telephone number which can be formed using last [tex]4[/tex] digits of phone number.

Now,

Total ways in which last [tex]4[/tex] digits can be arranged [tex]=4![/tex]

                                                                                 [tex]=4\times3\times2\times1[/tex]

                                                                                 [tex]=24[/tex]

Therefore we will have to make 24 calls in order to dial the correct number.

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