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 o

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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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Remi 1 month 2021-08-16T17:07:47+00:00 2 Answers 0 views 0

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    0
    2021-08-16T17:09:14+00:00

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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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    0
    2021-08-16T17:09:18+00:00

    \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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