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in Mathematics by (54.9k points)

How many 5-digit telephone numbers can be constructed using the digits 0 to 9 if each number starts with 67 and no digit appears more than once?

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Given : 0 to 9 digits (i.e., 10 digits) 

To find : number of 5-digit telephone numbers

There are 10 digits form 0 to 9 out of which 6 and 7 are fixed in first and second places respectively. Since the repetition of digits is not allowed, therefore the third, fourth and fifth places can be filled in 8, 7 and 6 ways respectively.

Hence five places can be filled in 8 x 7 x 6 ways i.e., 336 ways Required number of telephone numbers = 336

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