The total number of numbers that can be formed by using the digits 5, 3 and 7 only, if no repetitions are allowed, is:

Concept:

Basic Principle of Counting:

If there are m ways for happening of an event A, and corresponding to each possibility there are n ways for happening of event B, then the total number of different possibilities for happening of events A and B are:

• Either event A alone OR event B alone = m + n.
• Both event A AND event B together = m × n.

Calculation:

Since, the repetition is not allowed, we cannot form a four-digit or a higher digit number.

We have the following possible cases:

One-digit number:

There are three possibilities (3, 5, 7) for the single digit. ⇒ 3 possibilities.

Two-digit number:

There are three possibilities for one of the digits, and corresponding to each possibility, the other digit will have two possibilities. ⇒ 3 × 2 = 6 possibilities.

Three-digit number:

There are three possibilities for one of the digits, and then two possibilities for the second digit and then only a single possibility for the third digit. ⇒ 3 × 2 × 1 = 6 possibilities.

∴ The total number of possible numbers = 3 + 6 + 6 = 15.