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,

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,

➡️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:-

✴➡️(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,

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,

➡️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✔

Step-by-step explanation:

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