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How many four digit numbers can be formed from the digits 1,3,5,7,8 and 9 where a digit is used at most once?

A.if the numbers must be even?
B.if the numbers are less thsn 3000?
i need detail explanation ​

1 Answer

4 votes

Answer:

A. To form an even number, the last digit must be either 8 or 5, since they are the only even digits in the set. Since a digit can be used at most once, there are two choices for the last digit.

For the first digit, there are four choices (1, 3, 5, or 7), since we cannot use 0 or the last digit.

For the second digit, there are four choices remaining (since one digit has been used), and for the third digit, there are three choices left.

Therefore, the total number of four-digit even numbers that can be formed is: 2 x 4 x 4 x 3 = 96.

B. To form a number less than 3000, the first digit must be 1, 3, or 5. There are three choices for the first digit.

For the second digit, there are four choices remaining (since one digit has been used), and for the third digit, there are three choices left.

For the fourth digit, there are two choices remaining (since we cannot use the first digit).

Therefore, the total number of four-digit numbers less than 3000 that can be formed is: 3 x 4 x 3 x 2 = 72.

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