[Aptitude Q] PNC: How many natural numbers, below 1000 using 2,7,5,8,9 without repetition?

Question from a reader

How many natural numbers, below 1000, can be formed from the digits 2,7,5,8,9., if no digit is repeated.
Answer choices

1. 80
2. 85
3. 90
4. 95

Explanation

Do read my earlier article to under the approach in such questions. (click me)
Since we’ve to form numbers, the “order” matters, hence it is a permutation problem.
The biggest number that we can form is 987. (Three digit number)
Total number of natural numbers
=Single digit numbers AND double digit numbers  AND triple digit numbers
And means addition
=5P1 + 5P2 + 5P3
=5 + (5 x 4) + (5 x 4 x 3)
=5 + 20 + 60
=85 numbers can be formed.
Correct Answer choice (b)

Sidenote :If reparation was allowed then

=5 + (5×5) + (5x5x5)
=5+ 25 +125
=155