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. 

[Hint: Besides 4-digit integers greater than 7000, five digit integers are always greater than 7000.]

Answer 1

According to the question,

Digits that can be used = 3,5,7,8,9

Since, no digits can be repeated,

The number of integers is ⁵P₅ = 5! = 120

For a four-digit integer to be greater than 7000,

The four-digit integer should begin with 7,8 or 9.

The number of such integer = 3 × ⁴P₃ =3 × ⁴P₃ = 3(24) =72

Therefore, the total no of ways = 120+72 = 192