Find the number of integers greater than 7000 that can be formed with the digits 3, 5, 7, 8 and 9 where no digits are repeated.

We have to find the number of integers greater than 7000 with the digits 3,5, 7, 8 and 9. So, with these digits, we can make maximum five-digit numbers because repetition is not allowed.

Since all the five-digit numbers are greater than 7000, we have Number of five-digit integers = 5 x 4 x 3 x 2 x 1 = 120 A four-digit integer is greater than 7000 if thousandth place has any one of 7, 8 and 9.

Thus, thousandth place can be filled in 3 ways. The remaining three places can be filled from remaining four digits in ⁴P₃ ways.

So, total number of four-digit integers = 3x ⁴P₃ = 3 x 4 x 3 x 2 = 72 Total number of integers = 120 + 72 = 192

Given that all the 5 digit numbers are greater than 7000. 

So, the ways of forming 5-digit numbers = 5 × 4 × 3 × 2 × 1 = 120 

Now, all the four digit number greater than 7000 can be formed as follows. 

Thousand place can be filled with 3 ways 

Hundred place can be filled with 4 ways 

Tenths place can be filled with 3 ways 

Units place can be filled with 2 ways 

So, the total number of 4-digits numbers = 3 × 4 × 3 × 2 = 72 

∴ Total number of integers = 120 + 72 = 192 

Hence, the required number of integers = 192