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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 |
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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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