A product code in which order is important consists of a string of 4 different letters from the set {A, B, H, Q, T, Z}. How many codes contain the letters H, Q, or both?

Question

anonymous · Answer

this one is permutations i think

anonymous · Answer

ok that was totally wrong

anonymous · Answer

I get that you would permute since order matters, but I'm confused about multiplying by 2

anonymous · Answer

multiply by 2 because hq is different from qh

anonymous · Answer

ok maybe i am totally wrong, i best think

anonymous · Answer

lets try to think a bit more clearly
if it must contain h then you have 3 others to choose from out of the remaining 5, that is $\binom{5}{3}$ and then they can be permuted in $4!$ ways, giving $\binom{5}{3}\times4!$

anonymous · Answer

similarly for "it must contain q"

anonymous · Answer

and for "both" it we have already counted that in the above calculation

anonymous · Answer

Ok I think I got it, thanks again

anonymous · Answer

yw