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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Answer 1

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$\Large\fbox{\color{purple}{QUESTION}}$

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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✴➡️(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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Answer 2

Answer:

1)

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

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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.

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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