How many 4 digit nos greater than 2300 can be formed with digits 0,1,2,3,4,5 and 6, no digit being repeated in any number?
the given digits are 0,1,2,3,4,5,6, the number of given digits are 7.
1. taking the first 3 digits same 230 _ the fourth digit can be filled in 7-3 = 4 ways [as repetition is not allowed]
2. taking the first 2 digits same 23_ _ , 2nd last digit can be filled in 4 ways [ because we can not write 2,3,0 in 2nd last place] then remaining digits are 7-3 = 4 last place can be filled in 4 ways
therefore total number of ways = 4*4 = 16 ways
3. taking first digit 2 _ _ _ , 2nd place can be filled in 3 ways [ as we can write only digits greater than 3 in 2nd place i.e. 4, 5, 6 ] then 3rd place can be filled by remaining 5 digits and 4th place cen be filled by remaining 4 digits.
the number of ways = 3*5*4 = 60
4. taking the numbers more than 3000, thousands digit greater than or equal to 3.
therefore 1st place can be filled in 4 ways [ i.e. digits can be filled 3,4, 5,6]
the number of digits that are greater than 3000 [formed by the given digits]
= 4*6*5*4
=480
thus the total number of ways are 4+16+60+480
= 80+480
=560
hope this helps you
1. taking the first 3 digits same 230 _ the fourth digit can be filled in 7-3 = 4 ways [as repetition is not allowed]
2. taking the first 2 digits same 23_ _ , 2nd last digit can be filled in 4 ways [ because we can not write 2,3,0 in 2nd last place] then remaining digits are 7-3 = 4 last place can be filled in 4 ways
therefore total number of ways = 4*4 = 16 ways
3. taking first digit 2 _ _ _ , 2nd place can be filled in 3 ways [ as we can write only digits greater than 3 in 2nd place i.e. 4, 5, 6 ] then 3rd place can be filled by remaining 5 digits and 4th place cen be filled by remaining 4 digits.
the number of ways = 3*5*4 = 60
4. taking the numbers more than 3000, thousands digit greater than or equal to 3.
therefore 1st place can be filled in 4 ways [ i.e. digits can be filled 3,4, 5,6]
the number of digits that are greater than 3000 [formed by the given digits]
= 4*6*5*4
=480
thus the total number of ways are 4+16+60+480
= 80+480
=560
hope this helps you