How many four-digit odd numbers less than 6000 can be formed usin...

Question

How many four-digit odd numbers less than 6000 can be formed using the digits 2, 4, 6, 7, 8, and 9?

Accepted Answer

Hey, everyone here, we are asked to find the amount of numbers which are five digit even numbers greater than 90,000 and formed using the digits 23456 and nine. So to start solving this, we need to look at each digit and determine how many different choices of digits we can have. So, beginning with our first digit of our possible number. Well, we know that this five digit number must be greater than 90,000. So this first digit must be nine. So with this, we see that for our first digit, we can only have one choice and now moving on to our last digit because we are told we need an even number. We know that our last digit must also be an even number. So it can be either 24 or six. So with this, we know that our fifth digit is, has three different choices. Again, these are our uh number of choices here. And then for our 2nd, 3rd and 4th digits, they can be any of these numbers and we have a total of 123456 digits to choose from. So our 2nd 3rd and 4th digits have six different choices. And now all we have to do is multiply each of these variations together to find our solution. So, beginning with our first digit, we have one then times the second digit which is six choices and times the third, which also has six choices. And the fourth, it, which is also six and lastly times the fifth digit which has three choices. And now multiplying all these terms together, we see that we have a total number of 648 5 digit even numbers which are greater than 90,000 and again formed by these given digits. And therefore we are left with answer choice. D Thanks for watching. I hope you found this video helpful and I'll see you again next time.

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How many four-digit odd numbers less than 6000 can be formed using the digits 2, 4, 6, 7, 8, and 9?