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in Permutations by (46.3k points)
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How many seven-digit phone numbers are possible if 0 and 1 cannot be used as the first digit and the first three digits cannot be 555, 411 or 936?

(a) 412560 

(b) 7970000 

(c) 797000 

(d) 362880

1 Answer

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Best answer

(b) 7970000

For the first digit there are 8 choices (out of 10 digits) as 0 and 1 cannot be used. Since repetition can be done, the 2nd digit and the 3rd digit have 10 choices each. So, the first three digits can be filled in (8 × 10 × 10 – 3) ways (We need to exclude the numbers 555, 411 and 936 also from first three digits) 

The last four digits of the telephone number can be filled in (10 × 10 × 10 × 10) ways. 

∴ Total number of seven digit phone numbers = (8 × 10 × 10 – 3) × 10 × 10 × 10 × 10 = 7970000.

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