I use 16 because from what I gather that's the total number of female hairstyles available from Kerning City in v.54. That is including both VIP and EXP hairstyles. I suppose you used 21 because that's the number you find when you check how many hairstyles there are from https://bbb.hidden-street.net/cash-shop/beauty-parlor/ and thought I was only counting the VIPs. But that link includes some styles that shouldn't be in the current version of Phoenix.
Assuming you want a particular EXP hairstyle, a single EXP coupon always has a 1/16 chance to give you your desired hairstyle. This probability does not change unless we go to another hair salon or change the number of available haircuts. So, if we want our hairstyle we need to buy EXP coupons until one finally gives us the one we want. That is, with the 1/16 chance per coupon, we will have to buy 16 coupons on average to get our desired haircut.
Cash Shop has an infinite coupon supply, but our NX is not. If you had only 5700 NX, what would be the chances of you getting that EXP hair before your NX ran out? You can only afford 2 EXP coupons with that (2 * 2100 = 4200 NX), which is 2 chances of 1/16 (= 6.25%), which is a 12.5% chance in total.
However, if we lowered the price of EXP coupons, we could buy more EXP coupons. The cheaper the EXP coupons, the more we can buy. The more EXP coupons we buy, the more chances we get.
Let's assume again you spend 5700 NX (the price of a VIP coupon, for the sake of comparison) whether on VIP or EXP tickets and try to get a desired haircut:
If you want a VIP haircut you would buy 1 VIP coupon for 5700 NX and get your desired style with a 100% chance.
If you want an EXP haircut and spend the same amount of 5700 NX on EXP coupons, you will have bought ~2.71 coupons in total and your chance of getting your desired hairstyle would be ~17%.
Of course in a real setting, you wouldn't be able to buy exactly 2.71 coupons but 2 or 3 coupons, which come to 12.5% and 18.75% chances respectively. It would depend on how much NX you have.
If the price of an EXP coupon was 1425 NX instead of 2100, and we spent 5700 NX on them, we could buy 4 coupons and the chance would be 25%. If the price was 600 NX, and we only had 5700 NX to spend, we could afford 9 coupons and the chance of that would be 56.25%.