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

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»

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