How to Work Out Permutation Costs by Hand, Step by Step

Most players these days let an online perm calculator do the arithmetic, which is fine right up until it isn’t available, or you want to actually understand what the number it spits out means. Working out a permutation cost by hand is not difficult once you have the method, and it genuinely changes how you think about perm sizing once you have done it yourself a few times.

Why bother when calculators exist

A perm calculator will always be faster for day-to-day use, and nobody should feel obliged to do this by hand every single week. The reason it is worth learning anyway is that a calculator gives you an output with no visible working, which makes it hard to build any intuition for how adding or removing a single fixture changes your cost. Once you have worked through the method yourself a couple of times, that relationship stops being a mystery and starts being something you can estimate roughly in your head before you even open a calculator.

The formula you need

Choosing r selections to count from a pool of n fixtures — for instance, “any 8 count from these 11 fixtures” — is a classic combinations problem, written as C(n,r) or “n choose r”. The formula is:

C(n,r) = n! / (r! × (n-r)!)

Where “!” means factorial — multiply the number by every whole number below it down to 1. That looks intimidating written out in full, but in practice most of the factorial cancels out, which is the trick that makes hand calculation manageable.

Worked example 1: 6 from 9

Suppose you want any 6 correct from 9 selected fixtures. Set up the formula:

C(9,6) = 9! / (6! × 3!)

Here is the shortcut: instead of calculating 9! in full, write only the top part down to where it would cancel with 6!, since 9!/6! = 9 × 8 × 7 (the numbers from 9 down to 7, stopping once you reach 6):

9 × 8 × 7 = 504

Now divide by 3! (which is 3 × 2 × 1 = 6):

504 ÷ 6 = 84 lines

So “6 from 9” produces 84 lines — manageable with a pen and a few seconds of multiplication, no calculator app required.

Worked example 2: 8 from 11

Using the same shortcut method for “8 from 11”:

C(11,8) = 11!/(8! × 3!). The top part, 11!/8!, is 11 × 10 × 9 = 990. Divide by 3! = 6:

990 ÷ 6 = 165 lines

This matches the figure used elsewhere on this site for an 8-from-11 perm, confirming the method works consistently.

A trick for larger pools: use symmetry

One genuinely useful shortcut is that C(n,r) always equals C(n, n-r) — choosing 8 to count from 11 produces exactly the same number of lines as choosing which 3 to leave out of 11. For a case like “8 from 11”, recognising that 11-8=3 means you can calculate C(11,3) instead if that happens to involve smaller, friendlier numbers:

C(11,3) = 11 × 10 × 9 ÷ 3! = 990 ÷ 6 = 165, exactly the same answer as before, reached by multiplying three numbers instead of eight. Whenever r is more than half of n, flip to n-r and the sums get noticeably easier.

A step-by-step checklist for any perm

1. Write down n (total fixtures in your pool) and r (how many need to count).
2. If r is more than half of n, swap to n-r instead — same answer, smaller numbers.
3. Multiply the top part: start at n and count downward, multiplying as many numbers as your (possibly swapped) r value.
4. Calculate r! by multiplying r down to 1.
5. Divide the top-part total by r! to get your line count.
6. Multiply the line count by your chosen unit stake to get total cost.

Putting it together: costing a full perm

Take the 8-from-11 result of 165 lines. At an illustrative stake of 10p per line:

165 × £0.10 = £16.50 total outlay.

If you wanted a wider pool — say 8 from 12 — repeat the process: top part is 12 × 11 × 10 × 9 = 11,880, divided by 4! (24) gives 495 lines, costing £49.50 at the same stake. Running through the arithmetic yourself, rather than only reading the final number off a calculator, makes that jump from 165 to 495 lines feel like a concrete consequence of adding one fixture, rather than an abstract number you have to just trust.

A second worked example to build confidence

Try “9 from 13” as a further check on the method. Since 9 is more than half of 13, flip to the smaller side first: 13-9=4, so calculate C(13,4) instead. The top part is 13 × 12 × 11 × 10 = 17,160. Divide by 4! (24): 17,160 ÷ 24 = 715 lines. Running the same calculation the “long way” as C(13,9) — top part 13×12×11×10×9×8×7×6×5, divided by 9! — produces the same 715, but involves far more multiplication for no extra accuracy, which is exactly why the symmetry shortcut above is worth remembering.

Why doing it by hand is worth the effort once

Nobody is suggesting you calculate every weekly perm with pen and paper forever — a calculator or spreadsheet is faster and just as accurate for routine use. The value of working through the method by hand once or twice is that it makes the scaling behaviour of perms intuitive rather than mysterious. Once you have personally watched the top-part multiplication grow from three numbers to four as you add one fixture, the jump in cost stops feeling arbitrary and starts feeling like simple, predictable arithmetic — which is exactly what it is.

A responsible closing note

Understanding the maths behind a perm’s cost helps you budget accurately; it does not improve your chances of landing the outcomes you need, which remain governed by football itself rather than arithmetic. Decide your weekly spend in advance, use the method above to check a perm fits that budget before submitting your coupon, and treat pools play as entertainment rather than income. Play is for those aged 18 and over; free, confidential support is available from GamCare for anyone concerned about their spending.