How many four-digit even numbers can be formed from the set {0, 1, 2, 3, 4, 5, 6, 7} if repetition of digits is NOT allowed?1 pointA. 1470B. 750C. 720D. 540
Question
How many four-digit even numbers can be formed from the set {0, 1, 2, 3, 4, 5, 6, 7} if repetition of digits is NOT allowed?1 pointA. 1470B. 750C. 720D. 540
Solution
To solve this problem, we need to consider the conditions given:
- The number must be a four-digit number.
- The number must be even.
- Repetition of digits is not allowed.
Let's break it down:
-
The last digit of the number must be even. Since 0 is also an even number, we have 4 choices for the last digit (0, 2, 4, 6).
-
The first digit can be any of the remaining 7 digits (since it can't be 0 or the digit we chose for the last place). So, we have 7 choices for the first digit.
-
For the second digit, we can choose from the remaining 6 digits. So, we have 6 choices for the second digit.
-
For the third digit, we can choose from the remaining 5 digits. So, we have 5 choices for the third digit.
So, the total number of four-digit even numbers that can be formed is 7 (choices for the first digit) * 6 (choices for the second digit) * 5 (choices for the third digit) * 4 (choices for the last digit) = 840.
So, the correct answer is not listed in the options given.
Similar Questions
How many numbers can be formed using all the digits 1, 2, 3, 4, 3, 2, 1 such that even digits alwaysoccupy even plac
How many 7-digit even numbers less than 3 000 000 can be formed using all the digits1, 2, 2, 3, 5, 5, 6 ?
How many even numbers less than 500 can be formed using the digits 1, 2, 3, 4 and 5? Each digit may be used only once in any number.
How many different 4 digit numbers can be formed using the digits 1, 2, 5, 6, 7 and 8?Options36024120720
How many four-digit odd numbers can be formed with the digits 0-9 if each digit is used only once in each number?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.