Verified solution · Exam P
This Exam P sample reference tests Counting Methods. Choose the leading letter, place two additional distinct letters in two of the four remaining positions, and fill both digit positions independently. The count is 9.360 million, so choice E.
Independent solution
Setup
Choose the letter occupying the required leading position.
Model
Select two of the four open positions for the other letters, place two different letters there, and then fill the remaining positions with digits.
Compute
Multiply the independent placement counts and convert the result to millions.
Answer
The capacity is 9.360 million unique strings.
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Error diagnosis
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
Original practice · fully worked
A planner creates an ordered route of four distinct inspection sites chosen from nine available sites. Two particular sites cannot both appear on the same route. Calculate the number of permitted routes.
There are 9P4=3024 unrestricted routes. The two incompatible sites occupy two ordered positions in 4P2 ways, with the other positions filled in 7P2 ways, so 504 routes are excluded and 2520 remain.
Setup
Count all ordered four-site routes before imposing the incompatibility.
Model
For an invalid route, place the two particular sites in two ordered route positions and fill the other positions from the remaining seven sites.
Compute
Subtract the routes containing both incompatible sites from the unrestricted count.
Answer
There are 2520 permitted ordered routes.
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ActuaryProof. “SOA Exam P Sample Question #424 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
