Question

how many natural number not exceeding 4321 can be formed with the digits 1,2,3,4 if the digit can repeat ?

explain all steps ? ​

Answer 1

Answer:

229

Step-by-step explanation:

Taking only four digit numbers:

If we take numbers less than four thousand, then

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

Also, can you tell which previous question are your referring to -- Is it the one with forming 5 digit numbers using 1,2,3,4,5? In that case, we asked you if the digits were correct and you never clarified it. If you think the question is what you wrote it was, then please ask the query back and we will reply it accordingly.

Answer 2

1. 229 is your answer.......