Question

a person starts writing all the 4 digit numbers how many times he has written the digit 2?

Answer 1

36 is the answer to your question.

Answer 2

Answer:

answer is 3700

Step-by-step explanation:

4 digit number = _ _ _ _

STEP 1: if first digit is 2 then other 3 digits have 0-9 i.e 10 ways therefore total no. of ways for first digit =2 are 10*10*10=1000;

STEP 2 : now if 2nd digit is 2 ; then we have 1-9 options for first digit ( as if we put 0 at first digit it become 3 digit number ) and 3rd and 4th digit have 0-9 i.e 10 ways

therefore if 2nd digit is 2 we have ways= 9*10*10=900

STEP 3 : SIMILARLY as in STEP 2  : if 3rd digit is 2 ; then we have 1-9 options for first digit ( as if we put 0 at first digit it become 3 digit number ) and 2nd and 4th digit have 0-9 i.e 10 ways

therefore no. of ways for 3rd digit as 2 = 9*10*10=900;

STEP 4 : same as step 3:

now total number of ways = 1000+900+900+900=3700

When a = 2, b / c / d can be filled in 10 ways each.

So, 2 will appear in place of 'a' 10*10*10 = 1000 times

When b = 2, a can be filled in 9 ways whereas c / d can be filled in 10 ways each.

So, 2 will appear in place of 'b' 9*10*10 = 900 times

Similarly, 2 will appear in place of 'c' 900 times and in place of 'd' 900 times.

Total number of times digit '2' will appear = 1000 + 900 + 900 + 900 = 3700 times