How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that (i) Repetition of the digits is allowed? (ii

Question

How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that
(i) Repetition of the digits is allowed?
(ii) Repetition of the digits is not allowed?

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Piper 1 month 2021-08-16T17:32:29+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-08-16T17:33:36+00:00

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    How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that

    (i) Repetition of the digits is allowed?

    (ii) Repetition of the digits is not allowed?

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    ➡️(i) Let the 3-digit number be ABC, where C is at the units place, B at the tens place and A at the hundreds place.

    ➡️Now when repetition is allowed,

    ➡️The number of digits possible at C is 5. As repetition is allowed, the number of digits possible at B and A is also 5 at each.

    ➡️Hence, the total number possible 3-digit numbers =5 × 5 × 5 =125

    ➡️(ii) Let the 3-digit number be ABC, where C is at the units place, B at the tens place and A at the hundreds place.

    ➡️Now when repetition is not allowed,

    Now when repetition is not allowed,The number of digits possible at C is 5.

    ➡️Let’s suppose one of 5 digits occupies place C, now as the repletion is not allowed, the possible digits for place B are 4 and similarly there are only 3 possible digits for place A.

    ➡️Therefore,

    ➡️The total number of possible 3-digit numbers=5 × 4 × 3=60

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    0
    2021-08-16T17:34:23+00:00

    Answer:

    1)

    A three digit number is to be formed from given 5 digits 1,2,3,4,5.

    □□□

    HTO

    Now, there are 5 ways to fill ones place.

    Since, repetition is allowed , so tens place can also be filled by 5 ways.

    Similarly,hundreds place can also be filled by 5 ways.

    So, number of ways in which three digit numbers can be formed from the given digits is 5×5×5=125


    Alternative Method:

    There will be as many way ways as there are ways of filling 3 vacant places in succession by the given five digits. In this case, repetition of digits is allowed. Therefore, the units place can be filed  by any of the given 5 digits.

    Similarly, tens and hundreds digits can be filled in by any given 5 digits.

    Thus, by the multiplication principle, the number of ways in which three digit numbers can be formed from the given digits is 5×5×5=125


    ii) A three digit number is to be formed from given 5 digits 1,2,3,4,5.

    □□□

    HTO

    Now, there are 5 ways to fill ones place.

    Since, repetition is not allowed , so tens place can be filled by remaining 4 digits.

    So, tens place can be filled in 4 ways.

    Similarly, to fill hundreds place, we have 3 digits remaining.

    So,hundreds can be filled by 3 ways.

    So, required number of ways in which three digit numbers can be formed from the given digits is 5×4×3=60

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