How many different 4 digit numbers can be formed using the digits 1, 2, 5, 6, 7 and 8?Options12072036024

The problem can be solved using the concept of permutations.

Step 1: Understand the problem We are asked to find out how many different 4-digit numbers can be formed using the digits 1, 2, 5, 6, 7, and 8.

Step 2: Identify the number of digits We have 6 digits (1, 2, 5, 6, 7, 8) and we need to form a 4-digit number.

Step 3: Use the formula of permutations The formula for permutations is nPr = n! / (n-r)!, where n is the total number of options, r is the number of options chosen at a time, and '!' denotes factorial.

Step 4: Substitute the values into the formula Here, n = 6 (the number of digits) and r = 4 (the number of digits in the number to be formed). So, the number of permutations is 6P4 = 6! / (6-4)! = 6! / 2!

Step 5: Calculate the factorial values 6! = 654321 = 720 2! = 21 = 2

Step 6: Divide to get the answer So, 6P4 = 720 / 2 = 360

Therefore, 360 different 4-digit numbers can be formed using the digits 1, 2, 5, 6, 7, and 8.