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Home » In a certain city, all telephone numbers have six digits, the first two digits always being 41 or 42 or 46 or 62 or 64. How many telephone numbers have all six digits distinct?
In a certain city, all telephone numbers have six digits, the first two digits always being 41 or 42 or 46 or 62 or 64. How many telephone numbers have all six digits distinct?
CBSE | Class 11 | Maths | NCERT Exemplar | Permutations and Combinations
In a certain city, all telephone numbers have six digits, the first two digits always being 41 or 42 or 46 or 62 or 64. How many telephone numbers have all six digits distinct?

Solution:

As per the question,

All the telephone numbers have 6 digits

Provided that,

First 2 digits = 41 or 42 or 46 or 62 or 64

As a result, the no. of two digits that the telephone no. begins with =5

The first 2 digits can be filled in five ways,

The remaining four-digits can be filled in { }^{8} \mathrm{P}_{4} ways,

{ }^{8} \mathrm{P}_{4}=8 ! /(8-4) !=1680

As a result, no. of telephone nos. having 6 distinct digits =5 \times 1680 =8400

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