Question

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

Answer 1

3*4*3*2+3*4**3*2*1=144

Answer 2

Sol: 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 = 5x4x3x2x1 = 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 = 3x4x3x2 = 72 Total number of integers = 120 + 72 = 192