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4. A ten digit telephone number is of the form (XYZ)-ABC-DEFG. In one particular state, there
are 4 possible area codes (202, 341, 602, and 581). The digit 'A' is restricted to a number 2
through 8. The digits B and C can be any number but they cannot repeat. The digits D,E,F,
and G have no restriction. How many seven digit phone numbers are possible with these
restrictions?



Answer :

abiolataiwo2015

If  a ten digit telephone number is of the form (XYZ)-ABC-DEFG. The seven digit phone numbers that are possible with these restrictions is: 25,200,000 phone numbers.

Possible ways

XYZ=4 possible area code=C'4

'A'  number 2 through 8=C'7

B and C= C'10 C'9

D,E,F, and G= C'10 C'10 C'10 C'10

Hence,

Possible ways=C'4 C'7 C'10 C'9 C'10 C'10 C'10 C'10

Possible ways=4×7×10×9×10×10×10×10

Possible ways=25,200,000  phone numbers

Therefore If  a ten digit telephone number is of the form (XYZ)-ABC-DEFG. The seven digit phone numbers that are possible with these restrictions is: 25,200,000 phone numbers.

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