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If all of the telephone extensions in a certain company must be even numbers, and if each of the extensions is formed using the digits 1, 2, 3, and 6, what is the greatest number of four-digit extensions that the company can have (repetitions are allowed) ?
156
64
48
256
128
156
64
48
256
128
Solution
Four digit numbers has for spaces.
__ __ __ __
Since, extensions must be even numbers the units digit should be either 2 or 6.
The unit’s digit have 2 options.
Each of the remaining spaces has 4 options each (since repetition is allowed).
Hence, the total number of extensions that can be formed = 4 × 4 × 4 × 2 = 128
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