Question

Find the number of 4-digit numbers that can be formed using the digits 1, 2, 3, 4, 5 if no digit is repeated. How many of these will be even?

Answer 1

Answer:

nswer

(i)A four digit number is to be formed from the digits 1,2,3,4,5.

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HTO

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 5×4×3×2=120

(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 2×4×3×2=48

Step-by-step explanation: