Three employees need to visit 40 different cities under the following conditions: each location should be visited by exactly one employee, and no location should be visited multiple times. The travel agency should plan the tours for three employees. How many "tour" options are there in total?
Is the solution number of permutations with 3 cycles?
It seems that you want to partition the given set of $40$ distinguishable locations into $3$ nonempty blocks, without naming the blocks. The number of ways this can be done is the Stirling number of the second kind $S(40,3)$ (there are various notations in use). The resulting number is $$S(40,3)=2\,026\,277\,026\,753\,674\,246\ .$$