How many 5 digit telephone numbers can be constructed using the di | Filo

Class 11

Math

Algebra

Permutations and Combinations

579
150

How many digit telephone numbers can be constructed using the digits to if each number starts with and no digit appears more than once?

Solution: It is given that the 5-digit telephone numbers always start with 67.
Therefore, there will be as many phone numbers as there as ways of filling 3 vacant places by the digits 0-9, keeping in mind that the digits cannot be repeated.
The unit place can be filled by any of the digits from 0-9, expect digits 6 and 7.
Therefore, the unit 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 the multiplication principle, the required number of  ways in which 5- digit telephone  numbers can be constructed is
579
150

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