Question

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?​

Answer 1

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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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➡️Let the five-digit number be ABCDE.

➡️Given that first 2 digits of each number is 67.

➡️Therefore, the number is 67CDE.

➡️As the repetition is not allowed and 6 and 7 are already taken, the digits available for place C are 0,1,2,3,4,5,8,9.

➡️The number of possible digits at place C is 8.

➡️Suppose one of them is taken at C, now the digits possible at place D is 7.

➡️And similarly, at E the possible digits are 6.

➡️∴The total five-digit numbers with given conditions = 8 × 7 × 6 = 336.

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Answer 2

$\huge\purple\star\underline\mathfrak\pink{</em></strong><strong><em>ANSWER</em></strong><strong><em> :-}\purple\star$

➡️Given that first 2 digits of each number is 67.

➡️Therefore, the number is 67CDE.

➡️As the repetition is not allowed and 6 and 7 are already taken, the digits available for place C are 0,1,2,3,4,5,8,9.

➡️The number of possible digits at place C is 8.

➡️Suppose one of them is taken at C, now the digits possible at place D is 7.

➡️And similarly, at E the possible digits are 6.

➡️∴The total five-digit numbers with given conditions = 8 × 7 × 6 = 336.

Step-by-step explanation:

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