how many 4 digit numbers are there which have exactly 3 distinct digits?
Answers
Step-by-step explanation:
There are 9×9×8×7 4-digit numbers that have 4 different digits. There are 9×9×8 4-digit number that have 3 different digits. But this 3 different digits can be place on 6 different ways: aabc,abac,abca,baac,baca,bcaa, so we multiply the number of combintion by 6.
Permutation and Combination
We have to take digits from
Hence we have total of 10 digits. The condition here is exactly 3 digits should be distinct and one more condition automatically applied here is that 1st digit can't have 0.This means 2 digits will be repeater and 2 will be distinct.
The three case will be formed :
1) when unit digit is repeated
The way of select 1st three digits are .
(∵ 1st place have only 9 option except 0, 2nd place has 9 options except the digit at 1st place, 3td place have 8 option excluding 1st place and 2nd place.)
The 4th place can be same as either of the three digits used earlier , hence it will have 3 ways.
Total number of ways becomes ways.
2) when ten's digit is repeated
first, third and fourth digit can be selected in .
The 3rd place can be same as first 2 digits, earlier, hence it will be have 2 ways.
Total number of ways becomes ways.
3) when hundred's digit is repeated
first, third and fourth digit can be selected in .
The 2nd place can be same as first digit, earlier, hence it will be have 1 ways.
Total number of ways becomes ways.
Total number of ways will be
Hence required number of ways is 3888.