Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • In how many ways can the digits 0, 1, 2, 3, 4, and 5 be arranged to form a six-digit number, allowing repetition, where at least two digits are even?  

In how many ways can the digits 0, 1, 2, 3, 4, and 5 be arranged to form a six-digit number, allowing repetition, where at least two digits are even?

 

Option: 1

2536

 


Option: 2

4587

 


Option: 3

1249

 


Option: 4

8975


Answers (1)

best_answer

To find the number of ways the digits 0,1,2,3,4, and 5 can be arranged to form a six-digit number, allowing repetition, where at least two digits are even, we need to consider the different cases.

Case 1: Exactly two even digits:

There are 3 choices for the positions of the even digits and 2 choices for each even digit. The remaining positions can be filled with any of the remaining 4 odd digits. Therefore, there are 3 \times 2 \times 2 \times 4 \times 4 \times 4=384 possible arrangements in this case.

Case 2: Exactly four even digits:

There are 3 choices for the positions of the odd digits and 4 choices for each odd digit. The remaining positions can be filled with any of the even digits. Therefore, there are 3 \times 4 \times 4 \times 4 \times 3 \times 3=864possible arrangements in this case.

Case 3: All six digits are even:

In this case, there is only 1 possible arrangement, which is using all 6 even digits.

Therefore, the total number of possible arrangements is 384+864+1=1249.

It is important to note that repetition is allowed in this case, as the digits 0,1,2,3,4, and 5 can be used multiple times.

Posted by

mansi

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Latest Question