Find the number of integers greater than 7000 that can be formed with

1.	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» 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

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»

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