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  • How many unique six-digit numbers can be formed using the digits 1,2,3,4,5, and 6, allowing repetition, where the product of all digits is odd?Option: 1

How many unique six-digit numbers can be formed using the digits 1,2,3,4,5, and 6, allowing repetition, where the product of all digits is odd?

Option: 1

46,656.

 


Option: 2

72,458

 


Option: 3

32,152

 


Option: 4

24,789


Answers (1)

best_answer

To determine the number of unique six-digit numbers that can be formed using the digits 1,2,3,4,5, and 6 , allowing repetition, where the product of all digits is odd, we need to consider the following:

The product of all digits will be odd if and only if there is at least one odd digit present. Since all the given digits (1,3,5) are odd, we are guaranteed to have an odd product.

The first digit of the six-digit number can be any of the six given digits (1,2,3,4,5,6).
For the remaining five digits, we can choose any of the six given digits (1,2,3,4,5,6) since repetition is allowed.

Therefore, the total number of unique six-digit numbers that can be formed is

6 \times 6 \times 6 \times 6 \times 6 \times 6=46,656.

It is important to note that repetition is allowed in this case, as the digits 1,2,3,4,5, and 6 can be used multiple times.

Posted by

Pankaj Sanodiya

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