How many 4 digit numbers greater than 2300 can be formed with the d

1.	How many 4 digit numbers greater than 2300 can be formed with the digits 0,1,2,3,4,5 and 6 no digit being repeated in any number?
Answer» There are two cases, (i) First digit is greater than 2 (ii First digit is 2 Case : (i) First digit can be chosen from 3,4,5,6 so 4 possibilities, then next 3 digits can be selected from any 6 digits. = 4 × 6 × 5 × 4 = 480 Case : (ii) First digit is 2, second digit starts from 3, so it can be 3,4,5,6 so 4 possibilities. Now if any one digit of third and fourth digit can be 0 as no digit is repeated so it will be surely greater than 2300. So last two digits can be selected from any 5 digits. = 1 × 4 × 5 × 4 = 80 ∴ Total = 480 + 80 = 560.

How many 4 digit numbers greater than 2300 can be formed with the digits 0,1,2,3,4,5 and 6 no digit being repeated in any number?

Answer»

There are two cases, (i) First digit is greater than 2 (ii First digit is 2

Case : (i) First digit can be chosen from 3,4,5,6 so 4 possibilities, then next 3 digits can be selected from any 6 digits.

= 4 × 6 × 5 × 4 = 480

Case : (ii) First digit is 2, second digit starts from 3, so it can be 3,4,5,6 so 4 possibilities.

Now if any one digit of third and fourth digit can be 0 as no digit is repeated so it will be surely greater than 2300. So last two digits can be selected from any 5 digits.

= 1 × 4 × 5 × 4 = 80

∴ Total = 480 + 80 = 560.

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