Question
Find the number of -digit even numbers that can be formed using the digits if no digit is repeated. How many of those will be even?
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(i)A four digit number is to be formed from the digits 1,2,3,4,5.
Now, ones place can be filled in 5 ways.
Since, repetition is not allowed, tens place can be filled by remaining 4 digits.
So, there are 4 ways to fill ten's place.
Since, repetition is not allowed , so hundreds place can be filled by remaining 3 digits .
So, hundred's place can be filled in 3 ways.
Similarly, to fill thousand's place, we have 2 digits remaining.
So,thousand's place can be filled in 2 ways.
So, required number of ways in which four digit numbers can be formed from the given digits is
(ii) Now, for the number to be even , ones place can be filled by 2 or 4.
So, there are 2 ways to fill one's place.
Since, repetition is not allowed, so tens place can be filled by remaining four digits.
So, tens place can be filled in 4 ways.
Since, repetition is not allowed , so hundreds place can be filled by remaining 3 digits .
So, hundred's place can be filled in 3 ways.
Similarly, to fill thousand's place, we have 2 digits remaining.
So,thousand's place can be filled in 2 ways.
So, required number of ways in which four digit even numbers can be formed from the given digits is
Now, ones place can be filled in 5 ways.
Since, repetition is not allowed, tens place can be filled by remaining 4 digits.
So, there are 4 ways to fill ten's place.
Since, repetition is not allowed , so hundreds place can be filled by remaining 3 digits .
So, hundred's place can be filled in 3 ways.
Similarly, to fill thousand's place, we have 2 digits remaining.
So,thousand's place can be filled in 2 ways.
So, required number of ways in which four digit numbers can be formed from the given digits is
(ii) Now, for the number to be even , ones place can be filled by 2 or 4.
So, there are 2 ways to fill one's place.
Since, repetition is not allowed, so tens place can be filled by remaining four digits.
So, tens place can be filled in 4 ways.
Since, repetition is not allowed , so hundreds place can be filled by remaining 3 digits .
So, hundred's place can be filled in 3 ways.
Similarly, to fill thousand's place, we have 2 digits remaining.
So,thousand's place can be filled in 2 ways.
So, required number of ways in which four digit even numbers can be formed from the given digits is
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Question Text | Find the number of -digit even numbers that can be formed using the digits if no digit is repeated. How many of those will be even? |
Answer Type | Text solution:1 |
Upvotes | 150 |