How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 | Filo

Class 11

Math

Algebra

Permutations and Combinations

592
150

How many -digit numbers can be formed from the digits and assuming that.

i) Repetition of the digits is allowed?
ii) Repetition of the digits is not allowed?

Solution: 1)
A three digit number is to be formed from given 5 digits .

Now, there are ways to fill ones place.
Since, repetition is allowed , so tens place can also be filled by ways.
Similarly,hundreds place can also be filled by ways.
So, number of ways in which three digit numbers can be formed from the given digits is

Alternative Method:
There will be as many way ways as there are ways of filling 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 digits.
Similarly, tens and hundreds digits can be filled in by any given digits.
Thus, by the multiplication principle, the number of ways in which three digit numbers can be formed from the given digits is

ii) A three digit number is to be formed from given digits .

Now, there are ways to fill ones place.
Since, repetition is not allowed , so tens place can be filled by remaining digits.
So, tens place can be filled in ways.
Similarly, to fill hundreds place, we have digits remaining.
So,hundreds can be filled by ways.
So, required number of ways in which three digit numbers can be formed from the given digits is
592
150

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