How many different numbers from $1,2,7,8$ taking one,two,three and four digits no repetitions and how many of them are above $200$?

Question

Taking one, two, three and four digits from digits $1,2,7$ and $8$, and if repetitions are not allowed

1. How many different numbers can be arranged?
2. How many of them would be greater than $200$?

I got the first answer $= 64$:

• $4$ one digit numbers
• $12$ two digit numbers
• $24$ three digit numbers
• $24$ four digit numbers

total $= 64$

How to know how many are above $200$ though?

Answer 1

Your calculations for the firs question are correct. For the second, any $4$ digit number is $>200$ and any three digit number that starts with $2,7$ or $8$. Hence, $3$ out of $4$ three digit numbers are above $200$, which gives you a total of $$24+\frac{3}{4}24=42$$ numbers above 200.