Question

How many 4 digit natural numbers not exceeding 4321 gmat?

Answer 1

Answer:

Case 1: Four- digit number

Total number of ways in which the 4 digit number can be formed =4×4×4×4=256

Now, the number of ways in which the 4− digit numbers greater than 4321 can be formed is a s follows :

Suppose, the thousand's digit is 4 and hundred's digit is either 3 or 4.

∴ Number of ways =2×4×4=32

But 4311,4312,43413,4314,4321 are less than or equal to 4321

∴ Remaining number of ways =256−(32−5)=229

Case 2: Three- digit number

The hundred's digit can be filled in 4 ways.

Similarly, the ten's digit and the units digit can also be filled in 4 ways each.

This is because the repetition of digits is allowed.

∴ Total number of three- digit number =4×4×4=64

Case 3: Two- digit number

The ten's digit an the unit's digit can be filled in 4 ways each. This is because the repetition of digits is allowed.

∴ Total number of two digits numbers =4×4=16

Case 4: One- digit number

Single digit number can only be 4

∴ Required numbers =229+64+16+4=313

Step-by-step explanation:

hope it's helpful