How many positive integers greater than 5,000,000 can be formed using

How many positive integers greater than 5,000,000 can be formed using the digits 2, 3, 3, 5, 5, 6, 8?

Answer»

If 1^st digit number starts with 5, 6 and 8 then all formed numbers by using given digits are greater than 5000000.

case I: If number starts with digit 5

Possible numbers = 6!/2! = 720/2 = 360

Case II: If number starts with digit 6

Possible numbers = 6!/2!2! = 720/4 = 180

Case III: If number starts with digit 8

possible numbers = 6!/2!2! = 720/4 = 180

\(\therefore\) Total number of positive integers which is greater than 5000000 and formed by using digits 2,3,3,5,5,6,8

= 360 + 180 + 180 = 720

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