How many numbers between 2000 and 5000 can be made from the digits 1, 2, 4, 5, 7 and 8 if each digit is used only once?

1 Answer
Shwetank Mauria
Mar 5, 2018

We can have #120# such numbers.

Explanation:

As the number is between #2000# and #5000#, it means the digit in thousand's place is either #2# or #4#.

If digit in thousand place is #2#, we can have #1,4,5,7,8# in hundred's place, ten's place and unit's place. We can choose three digits out of five in #P_3^5=5xx4xx3=60# ways.

Similarly if digit in thousand place is #4#, we can have #1,2,5,7,8# in hundred's place, ten's place and unit's place and we can choose three digits out of five in #P_3^5=5xx4xx3=60# ways.

Hence, in all we can have #120# such numbers.

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