Question

A student is asked to form numbers between 3000 and 9000 with digits 2, 3, 5, 7 and 9. if no digit is to be repeated, in how many ways can the student do so

Answer 1

Given:

Numbers formed should be in between 3000 and 9000

Digits: 2, 3, 5, 7, 9

Repetition is not allowed.

To find:

In how many ways can the student do so?

Solution:

The first digit cannot be 2 because we need a number greater than 3000.

Also, the first digit cannot be 9 because we need a number smaller than 9000.

So, in the first place, the only remaining options are 3, 5, or 7

                                3/5/7   ____   ____   ____

Number of options:   3         4          3         2

So, 3 × 4 × 3 × 2 = 72

Therefore, the student can do so in 72 different ways.