Regional MO 2016 Dhaka ques 8

[Md. Rifat uddin]

How many eight digit number can be formed by using the digits $1, 2, 3, 4, 5, 6, 7,8$ so that each number has $6$ digits in such place where that digit is less than the next digit?

Example: In number $2314; 2,1$ are two digits such that each of them is less than the next digit.

[super boy]

I think the answer is $7$

Solution: (If anyone check this if it's wrong or not, I'll be happy )

Notice when the symbol $ "<" $ is inserted in the appropriate place which is between the eight digits, there are $7$ place to put that symbol inside the eight digits. Also we've given a condition that "each number has $6$ digits in such place where that digit is less than the next digit", so I've to put $6$ symbols in that $7$ places. I can do that $\binom{7}{6} = 7$ such ways. And that's the answer I think. :/

[Nodee Haque]

isn't the answear (7+6) = 13 ? since, in the question it said how many 'numbers' can be formed. doesn't it mean that there would be different permutations after choosing the 6 digits?? i'm not sure though...

[samiul_samin]

Double post.See here