Question

How many plates of vehicles consisting 4 different digits can be made out of the integers 4,5,6,7,8,9?

Answer 1

Answer:

Step-by-step explanation:

Two answers are possible.

One is with the repetition of digits.

The other is without repetition of digits.

ANSWER 1: With Repetition

Numbers: 1,2,4,5,7,8

There are 4 digits __ __ __ __

1st digit can be filled by any of the 6 numbers.

Similarly 2nd, 3rd and 4th digits.

Hence each digit will have 6 possibilities.

Therefore no.of 4 digit numbers that can be formed are 6 x 6 x 6 x 6 = 1296

ANSWER 2: Without Repetition

4 digits __ __ __ __

Now the first digit can be filled by any of the six numbers. Therefore there are 6 possibilities

The second digit will have only 5 possibilities as one of the numbers gets used up by the 1st digit.

Similarly the 3rd and 4th digits will have 4 and 3 possibilities respectively.

Therefore no.of 4 digit numbers that can be formed are 6 x 5 x 4 x 3 = 360

Answer 2

Given: Plates of vehicles consisting 4 different digits are made out of the integers 4,5,6,7,8,9

To find: Number of such plates of vehicles

Explanation: Total number of digits= 6

The number plates consists of four different digits. No number is repeated in the number plates.

Now, the first digit can be filled in 6 different ways. Any of the given digits can be used.

When filling the second digit, we have only 5 options because 1 of the digits is already used.

Similarly the third digit can be filled in 4 ways as 2 of them are used and the last digit can be filled in 3 ways.

Multiplication principle of permutations states that if one thing can be done in m ways and the other thing can be done in n ways, total number of ways is m× n.

Using this principle:

Total number of ways

= 6×5×4×3

= 360

Therefore, 360 plates of vehicles consisting 4 different digits can be made out of the given 6 numbers.