Class 11

Math

Algebra

Permutations and Combinations

How many numbers can be made with the digits $3,4,5,6,7,8$ lying between $3000$ and $4000$, which are divisible by $5$ while repetition of any digit is not allowed in any number?

- $60$
- $12$
- $120$
- $24$

Since the number lie between $3000$ and $4000$, the thousands place digit has to be $3$,

Now, the middle 2 digits van be chose from the remaining 4 digits (namely $4,6,7$ and $8$) in $_{4}P_{2}=2!4! =4×3=12$ ways.