Question

How many natural numbers of four digits can be formed if the digits are 2,3,5,0 repetitions are not allowed

Answer 1

Answer:

Clearly, with digits 5, 4, 3 and 2; we can form (4*4*4*4) = 256 four-digit numbers - out of which [1*1*4*4] = 16 are larger than 5432. (Only those are larger than 5432; who have 5 at thousand’s and hundred’s places both).

So, total number of four-digit numbers not exceeding 5432 = (256 - 16) = 240.

Now, three-digit, two-digit and single digit numbers all are smaller than 5432.

Number of three-digit numbers can be formed with digits 5, 4, 3 and 2 = (4*4*4) = 64.

Number of two-digit numbers can be formed with digits 5, 4, 3 and 2 = (4*4) = 16.

Number of single-digit numbers can be formed with digits 5, 4, 3 and 2 = 4.

Therefore, with digits 5, 4, 3 and 2; we can form (240 + 64 + 16 + 4) = 324 natural numbers.

hope it will help you

Answer 2

Answer:

The number of 4 digit natural numbers that can be formed is 18.

Step-by-step explanation:

This is a problem of Permutations and Combinations.

Given digits are 2, 3, 5, 0.

In order to create a 4 - digit number,

1. Repetition of digits is not allowed.
2. All the given digits should be used at a time.
3. The number 0 should not appear in the first position or in thousands position.

Using the above rules, calculate the number of 4 - digit natural numbers possible. The possible ways are given below:

1. The thousands position can be filled in 3 ways by (2,3,5). Then,

• The hundreds position can be filled in following way:

          1000's - 2, 100's - 3, 5, 0,  ways - 1*3 = 3

          1000's - 3, 100's - 2, 5, 0,  ways - 1*3 = 3

          1000's - 5, 100's - 2, 3, 0,  ways - 1*3 = 3

• The 100s position can be filled by 3 numbers in 9 possible ways
• Similarly, the 10s position can be filled with 2 numbers in  

          3*2 + 3*2 + 3*2 = 18  

• The units place can be filled in 1 way.

Therefore the number of 4 digit natural numbers that can be formed

 =  3 * 3 * 2 * 1 = 18

           

Therefore the number of 4 digit natural numbers that can be formed is 18.

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