Permutation Combination Question 11

Question 11 - 29 January - Shift 2

The total number of 4-digit numbers whose greatest common divisor with 54 is 2 , is ________

Show Answer

Answer: 3000

Solution:

Formula: Non-Consecutive Selection

$N$ should be divisible by 2 but not by 3

$N=($ Numbers divisible by 2$)-($ Numbers divisible by 6 )

$N=\frac{9000}{2}-\frac{9000}{6}=4500-1500=3000$