how many 4 digit number can be formed from the digits 2,3,5,,6,7,8 if:

a.)each digit be only used once
b) how many are even?
c) how many are odd?
d) how many are greater than 25000?

To solve this problem, you can use the concepts of permutations and combinations.

a.) To determine how many 4-digit numbers can be formed from the given digits, where each digit is used only once, we can apply the concept of permutations. In this case, we have 6 digits to choose from for the first position, 5 digits to choose from for the second position, 4 digits to choose from for the third position, and 3 digits to choose from for the fourth position. Therefore, the total number of 4-digit numbers can be calculated as: 6 * 5 * 4 * 3 = 360.

b.) To determine how many of these 4-digit numbers are even, we need to consider the last digit. In this case, the last digit can only be 2, 6, or 8, as these are the only even digits given. For the first position, we can choose any of the 3 even digits. For the remaining positions (second, third, and fourth), we can still choose from the 5 remaining digits. Applying the concept of permutations again, the total number of even 4-digit numbers can be calculated as: 3 * 5 * 4 * 3 = 180.

c.) To determine how many of these 4-digit numbers are odd, we can follow a similar process as in part b. In this case, the last digit can only be 3, 5, or 7, as these are the only odd digits given. For the first position, we can choose any of the 3 odd digits. For the remaining positions (second, third, and fourth), we can still choose from the 5 remaining digits. Applying the concept of permutations once again, the total number of odd 4-digit numbers can be calculated as: 3 * 5 * 4 * 3 = 180.

d.) To determine how many of these 4-digit numbers are greater than 25000, we need to consider the first digit. In this case, the first digit can only be 5, 6, or 7, as these are the only digits greater than 2 in the given set. For the first position, we can choose any of the 3 digits. For the remaining positions (second, third, and fourth), we can choose from any of the 5 remaining digits. Applying the concept of permutations once again, the total number of 4-digit numbers greater than 25000 can be calculated as: 3 * 5 * 4 * 3 = 180.