Question

how many four digit natural numbers not exceeding the number 4321 can be formed using the digits 1 2 3 4 everybody is allowed​

Answer 1

║⊕ANSWER⊕║

Taking only four digit numbers:

If we take numbers less than four thousand, then  the first place can be filled in 3 ways , 2nd place in 4 ways , 3rd in four ways and the fourth in four ways

Total such numbers = 3 x 4 x 4 x 4 = 192  

Now consider numbers starting with 4 and hundreds place either 1 or 2 (as the number has to be less than 4321)

So again for such numbers , first place can be filled in 1 way, 2nd place in 2 ways , third in 4 and fourth in 4 ways  .

Total such numbers = 1 x 2 x 4 x 4 = 32  

Now consider numbers that start with 4 , then followed by 3 . Now for such numbers there are two cases:  

Case 1 : 432 _  .. now this dash could be filled by only one number and i.e. 1  

Case 2 : 431_  .  now this dash can be filled in 4 ways .  

Total such numbers = 1+4 = 5  

In all  = 192 + 32 + 5 = 229

Answer 2

Step-by-step explanation:

313 is the answer hope it helps