How many 5-digit telephone numbers can …
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Naveen Sharma 8 years, 2 months ago
It is given that the 5-digit telephone numbers always start with 67.
Therefore, there will be as many phone numbers as there are ways of filling 3 vacant places.
by the digits 0 – 9, keeping in mind that the digits cannot be repeated.
The units place can be filled by any of the digits from 0 – 9, except digits 6 and 7.
Therefore, the units place can be filled in 8 different ways following which,
the tens place can be filled in by any of the remaining 7 digits in 7 different ways, and
the hundreds place can be filled in by any of the remaining 6 digits in 6 different ways.
Therefore, by multiplication principle, the required number of ways in which 5-digit telephone numbers can be constructed is 8 × 7 × 6 = 336
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