A fisherman can see seven aquatic creatures in a lake --- four crocodiles, a catfish, and two giant squid. If he does not wish to fish two crocodiles consecutively, in how many orders can he catch all seven creatures? (Individuals from the same species are indistinguishable.)
+6248 \(\text{We need to buffer crocodiles on each side with some other creature}\\ \text{As there are 4 crocodiles the only way this can be done is to have the crocs }\\ \text{occupy slots 1 3 5 7}\\ \text{having done this we can choose a slot for the catfish from the 3 remaining slots}\\ \text{That fixes the positions of the squid}\\ \text{Thus there are only 3 arrangements that satisfy no consecutive crocs}\)
.+6248 \(\text{We need to buffer crocodiles on each side with some other creature}\\ \text{As there are 4 crocodiles the only way this can be done is to have the crocs }\\ \text{occupy slots 1 3 5 7}\\ \text{having done this we can choose a slot for the catfish from the 3 remaining slots}\\ \text{That fixes the positions of the squid}\\ \text{Thus there are only 3 arrangements that satisfy no consecutive crocs}\)
