How many three-digit numbers are there with 3 in the unit place?(i) wi

1.	How many three-digit numbers are there with 3 in the unit place?(i) with repetition(ii) without repetition
Answer» (i) The unit place is filled (by 3) in 1 way The 10’s place can be filled in 10 ways The 100’s place can be filled in 9 ways (excluding 0) So the number of 3 digit numbers with 3 unit – place = 9 × 10 × 1 = 90 (ii) The digits are 0, 1,2, 3, 4, 5, 6, 7, 8, 9 A three digit number has 3 digits l’s, 10’s and 100’s place. The unit place is (filled by 3) filled in one way. After filling the unit place since the digit ‘0’ is there, we have to fill the 100’s place. Now to fill the 100’s place we have 8 digits (excluding 0 and 3) So 100’s place can be filled in 8 ways. Now to fill the 10’s place we have again 8 digits (excluding 3 and any one of the number) So 10’s place can be filled in 8 ways. ∴ Number of 3 digit numbers with ‘3’ in unit place = 8 × 8 × 1 = 64

How many three-digit numbers are there with 3 in the unit place?(i) with repetition(ii) without repetition

Answer»

(i) The unit place is filled (by 3) in 1 way

The 10’s place can be filled in 10 ways

The 100’s place can be filled in 9 ways (excluding 0)

So the number of 3 digit numbers with 3 unit – place = 9 × 10 × 1 = 90

(ii) The digits are 0, 1,2, 3, 4, 5, 6, 7, 8, 9

A three digit number has 3 digits l’s, 10’s and 100’s place.

The unit place is (filled by 3) filled in one way.

After filling the unit place since the digit ‘0’ is there, we have to fill the 100’s place. Now to fill the 100’s place we have 8 digits (excluding 0 and 3)

So 100’s place can be filled in 8 ways.

Now to fill the 10’s place we have again 8 digits (excluding 3 and any one of the number)

So 10’s place can be filled in 8 ways.

∴ Number of 3 digit numbers with ‘3’ in unit place

= 8 × 8 × 1 = 64

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