Question

how many five digit numbers can make by starting with 5 without repeating the numbers from 0 to 5

Answer 1

Step-by-step explanation:

This is a pretty straightforward question. Infact, if you know the approach to solve this problem, you can solve similar such problems with ease.

Had there been restrictions on the five digit numbers, like the number has to be even or odd or the number has to be divisible by 9 etc, it would not have been simple. Towards the end of this answer, I've provided a list of my solutions for similar problems, which have little complexity. You may refer them for a structured approach.

Anyways coming to this question,

# all 5digit numbers with no repetitions:

Ten thousands place can be filled up in 9ways , because zero can not be in this place, otherwise such number would be a 4digit number. Hence this position can be filled up with any one of 1–9 digits.

Thousand’s place can be filled up in 9ways , since we used one digit for units place and also there is no restriction for zero in this place.

hundred’s place can be filled up in 8ways

ten’s place can be filled up in 7ways

Units place can be filled up in 6ways .

Summing it up, we have 9∗9∗8∗7∗6(27,216) possible 5digit numbers with no digits repeating.

So answering this question, we have a total of 27,216 5−digit numbers with no repetition of digits.

Hope my explanation is simple and clear.

Answer 2

Concept: The integers on the number line that start at 10,000 and go up to 99,999 are known as 5 digit numbers. In their numeric form, these numerals have a total of 5 digits.

Given: 5- digit numbers starting with 5 without repeating numbers from 0-5.

To find: No. of 5- digit numbers

Solution:

Five digit number includes places till ten thousand, i.e.,

Ten thousand   Thousand   Hundred   Tens   Ones

Now, according to question, numbers are starting with 5, therefore at the place of ten thousand we fill the number 5

Ten thousand   Thousand   Hundred   Tens   Ones

5 (1 digit fixed)

Now, the numbers are not being repeated from 0 to 5, so we have the possibility of filling only 4 digits ( 6,7,8,9) at thousands, hundreds, tens and ones place, i.e.,

Ten Thousand   Thousand   Hundred   Tens            Ones

5 (1 digit fixed)     4 digits      4 digits      4 digits        4 digits

Therefore, possibility of 5 digit numbers are 1 × 4 × 4 × 4 × 4 = 256.

Hence, only 256 5-digit numbers can be made starting with 5 without repeating the digits from 0-5.

#SPJ2