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  • 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.]

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.]

Answers (1)

Since, repetition is not allowed a maximum of 5- digit numbers can be formed with digits 3, 5,7, 8 and 9.

Since, all the 5-digit numbers are greater than 7000 the number of 5-digitintegers= 5*4*3*2*1=120

A 4-digit number is greater than 7000 if thousandth place has any of the 7,8 and 9. The remaining 3 places can be filled from remaining 4 digits in ^4P_3 ways

So, total number of 4-digit integers = 3*^4P_3=3*4*3*2 =72 

Total number of integers=120+72 =192

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infoexpert21

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