How many 4-digit numbers are there with no digit repeated?​

Question

How many 4-digit numbers are there with no digit repeated?​

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Ariana 1 month 2021-08-16T16:14:47+00:00 2 Answers 0 views 0

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    0
    2021-08-16T16:16:04+00:00

    There are 4537 four digit-numbers with no digit repeated.
    Explanation :
    So we have 10 numbers, which are 0,1,2,3,4,5,6,7,8,9.
    And we have to make four digit numbers with no reputation.
    So we have four places which are THOUSANDS – HUNDREDS – TENS – ONES, for ONES place we have 7 ways of filling numbers ; for TENS place we have 8 options left; for HUNDREDS place we have 9 options ; for THOUSANDS we have 9 options left.
    By the PRINCIPLE OF COUNTING,

    When there are m ways to do one thing,
    and n ways to do another,
    then there are m×n ways of doing both.

    So, we have four ways which are 9*9*8*7, on multiplying, we will get our answer which is 4537
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    0
    2021-08-16T16:16:09+00:00

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    How many 4-digit numbers are there with no digit repeated?

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    ➡️To find four digit number (digits does not repeat)

    ➡️Now we will have 4 places where 4 digits are to be put.

    ➡️So, at thousand’s place = There are 9 ways as 0 cannot be at thousand’s place = 9 ways

    ➡️At hundredth’s place = There are 9 digits to be filled as 1 digit is already taken = 9 ways

    ➡️At ten’s place = There are now 8 digits to be filled as 2 digits are already taken = 8 ways

    ➡️At unit’s place = There are 7 digits that can be filled = 7 ways

    ➡️Total Number of ways to fill the four places = 9 × 9 × 8 × 7 = 4536 ways.

    ➡️So a total of 4536 four digit numbers can be there with no digits repeated.

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