Hello. This lesson will cover a few examples to help you understand much better the basic principles the counting.

You are watching: How many 3 digit numbers can be formed with repetition

** Example 1 **Find the variety of 3-digit numbers developed using the number 3, 4, 8 and, 9, such the no digit is repeated.

**Solution **The ‘task’ of forming a 3-digit number deserve to be separated into 3 subtasks – filling the hundreds place, filling the tens place and filling the units ar – every of which must be carry out to complete the task.

Now there space 4 ways to finish the very first subtask (i.e. Filling the thousands place), since we have 4 number to start with.

** **Next, there are 3 ways to finish to to fill the tens place (the second subtask), as currently there are only 3 number left to be offered (repetition the digits isn’t allowed). Lastly, there space 2 ways to complete the third task.

Therefore the total variety of ways to complete the task (which amounts to the required variety of 3-digit numbers) will certainly be 4 x 3 x 2 = 24. Nice neat.

Note that the digits could have been filled in any type of order, no necessarily in the order which ns did. The answer acquired would have actually been the same.

** Example 2 **How plenty of 3-digit numbers have the right to be formed using the digits 4, 5 and 6, such the the digit can repeat?

**Solution **This seems similar. However this time the number of ways to to fill the hundreds, tens and also the units location would it is in 3 in every case, (and not 3, 2, 1) because the digits are allowed to it is in repeated.

Therefore the number of such 3-digit numbers would be 3 x 3 x 3 = 27. I’ll list them the end again.

444 445 446 454 455 456 464 465 466 544 545 546 554 555 556 564 565 566 644 645 646 654 655 656 664 665 666

Okay. Let’s move on come a tiny more facility problems. Ok stick come counting number in this lesson.

** Example 3 **Find the number of 5-digit also numbers formed using the number 1 come 9, such the repetition of number is

(i) allowed

(ii) no allowed

**Solution **I imply that friend grab a pen / paper and shot to compute the prize yourself prior to reading further.

(i) In this case we have a restriction on filling the systems place, as the number needs to be even. Over there are just 4 methods to execute so (using 2, 4, 6 or 8).

For the other four places, we have 9 options each (as repetition is allowed).

Therefore the number of ways will certainly be 9 x 9 x 9 x 9 x 4 = 32805 (I won’t perform the numbers this time. You have no option but to believe me.)

(ii) This one is a little tricky. You could say that the answer is 9 x 8 x 7 x 6 x **4**, together there will certainly be 4 ways to fill the critical digit (using 2, 4, 6 or 8).

But yes sir a problem. We’re not certain that after filling the very first four locations (from the left), whether we’ll be left with 4 options for the units location or not. Due to the fact that one the the also digits could have already been used prior to we reach the devices place.

To get roughly this problem, us fill the devices place an initial using the even digits, followed by 8, 7, 6 and also 5 selections respectively because that the remaining places.

Therefore the number of such 5-digits numbers will be 4 x 8 x 7 x 6 x 5 = 6720.

** Example 4 **Find the variety of 4-digit weird numbers formed using the digits 0 to 9 such that repetition of number is

(i) allowed

(ii) no allowed

**Solution **The systems digit in this case can be filled in 5 means (using the strange digits). Now, there are only 9 means to to fill the thousands place, together 0 can not be supplied there. The remaining places deserve to be fill 10 methods each.

Therefore the full numbers in this instance would be 9 x 10 x 10 x 5 = 4500.

(Note that this is half of the full 9000 4-digit numbers possible, the other fifty percent being even)

(ii) We’ll very first fill the units ar with an odd digit – 5 ways. Next we have the thousands number – 8 means (leaving the end the 0).

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Finally, 8 means for the hundreds location (the 0 is back) and 7 methods for the 10s place. The full number will certainly be 5 x 8 x 8 x 7 = 2240

I assumption: v that’ll be it because that this lesson. Together a practice problem try and count the variety of 5-digit even numbers utilizing the number 0 come 9, with and also without repetition.

The next lesson will establish a couple of formulae / expressions to transaction with details situations. See you there!