Question

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

Answer 1

Heya!
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♦Permutations ♦
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⭐Digits - 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9


-> Five - Digit Number starting with 67 ,


↪Number of possible Arrangements =


As first two places are fixed , rest three numbers can be arranged as


- 8 × 7 × 6


=> 336 ways !!


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Answer 2

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