How many permutations of digits 012345and 6 either start wit

How many permutations of digits 0,1,2,3,4,5,and 6 either start with a 3 or end with 6?

Solution

We have total 7 digits and the condition is that the number should start with a 3 or end with a 6. So the position of 3 and 6 is fixed. 3 should be the first and 6 should be the last.

Now we are left with 5 digits which can be rearranged by 5! ways = 120 ways

Therefore number of permutations = 120 ways