Question

challenge

A number of four different digits is formed by using the digits 1,2,3,4,5,6 in all possible ways. Find how many of them are greater than 4500??​

Answer 1

Answer:

1000

Step-by-step explanation:

If the number has to be greater than 3400 then obviously the first digit of the number should be greater than or equal to 3 and the second digit should be greater than or equal to 4.

Therefore, possible permutations for first digit are: 3,4,5,6 and 7 ( total =5)

Case 1: If first digit is 3,

Possible permutations for 2nd digit are: 4,5,6 and 7 (total =4)

Case 2: If the first letter is greater than 3,

Possible permutations for 2nd digit are total 6 in number (1–7 excluding the number at first position)

Possible permutations for 3rd digit are total 5 in number (1–7 excluding the number at first and second position)

And for fourth, it will be 4 (1–7 excluding the number at first, second and third position).

Therefore, in case 1, total no of possible combinations = 5*4*5*4 = 400

And, in case 2, total no of possible combinations = 5*6*5*4 = 600.

So total no of possible numbers greater than 3400 =400+600 = 1000