# Total Number Of Combinations For A Loadout

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Now that the multiplayer portion of Warframe is currently down, I just went around doing Solo missions, until I was slightly bored and started to think of mathematics again. This led me to one question:

How many combinations of loadouts will there be for the player, assuming that the player starts as of 2014-08-02?

So, after checking out the Codex (and the Warframe Wiki) and getting the numbers, I found out that a new player (as of now) will have access to 142 weapons, 25 Warframes, 11 Companions and 7 Sentinel Weapons. Thus, the total number of combinations for making a loadout will be (if Kubrows take up the companions slot):

nCr(142, 1) * nCr(25, 1) * nCr(4, 1) = 14,200

If Sentienls take up the companions slot:

nCr(142, 1) * nCr(25, 1) * nCr(7, 1) * nCr(7, 1) = 173,950

That means the total number of combinations for making a loadout is:

173,950 + 14,200 = 188,150

That is, frankly, quite a lot.

And sorry for this. I was rather bored out of my skull.

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it reminds of borderlands, it has about 17.750.000 different guns

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You forgot about unequipping weapons/companions. Also there are 143 available weapons at the moment (45 primary, 43 secondary and 55 melee), because Boar is available as a part of the Wrecking Rhino Pack (I just checked the market). And new player can pick new starter weapons and buy/craft the old ones.

So the actual number is 25 (warframes) * (7 * 7 + 4 + 1) (companions/their weapons) * ( (46 + 1) (primary) * (44 + 1) (secondary) * (56 + 1) (melee) - 1) = 162 747 900.

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You forgot about unequipping weapons/companions. Also there are 143 available weapons at the moment (45 primary, 43 secondary and 55 melee), because Boar is available as a part of the Wrecking Rhino Pack (I just checked the market). And new player can pick new starter weapons and buy/craft the old ones.

So the actual number is 25 (warframes) * (7 * 7 + 4 + 1) (companions/their weapons) * ( (46 + 1) (primary) * (44 + 1) (secondary) * (56 + 1) (melee) - 1) = 162 747 900.

Actually, you seem to be also off with your calculations (and I assume a full loadout in my calculations up there). You forgot to split them into cases:

Case 1: Warframe + Primary = 25 * 46 (MK-1 included) = 1,150 (4,600 with Kubrows)

Case 2: Warframe + Secondaries = 25 * 44 (MK-1 included) = 1,100 (4,400 with Kubrows)

Case 3: Warframe + Melee = 25 * 56 (MK-1 included) = 1,400 (5,600 with Kubrows)

Case 4: Warframe + Primary + Sentinel = 25 * 46 * 7 = 8,050

Case 5: Warframe + Primary + Sentinel + Sentinel weapon = 56,350

Case 6: Warframe + Secondary + Sentinel = 25 * 44 * 7 = 7,700

Case 7: Warframe + Secondary + Sentinel + Sentinel weapon = 25 * 44 * 7 * 7 = 53,900

Case 8: Warframe + Melee + Sentinel = 25 * 56 * 7 = 9,800

Case 9: Warframe + Melee + Sentinel + Sentinel weapon = 68,600

Case 10: Warframe + Primary + Secondary = 25 * 46 * 44 = 50,600 (354,200 with Sentinel, 2,479,400 with Sentinel + weapon) (202,400 with Kubrows)

Case 11: Warframe + Primary + Melee = 25 * 46 * 56 = 64,400 (450,800 with Sentinel, 3,155,600 with Sentinel + weapon) (257,600 with Kubrows)

Case 12: Warframe + Secondary + Melee = 25 * 44 * 56 = 61,600 (431,200 with Sentinel, 3,018,400 with Sentinel + weapon) (246,400 with Kubrows)

Case 13: Warframe + Primary + Secondary + Melee = 25 * 46 * 44 * 56 = 2,833,600 (19,835,200 with Sentinels, 138,846,400 with Sentinels + weapons) (11,334,400 with Kubrows)

So, the total is 183,844,850. 183,844,850 total combinations for making a loadout.

I probably forgot to split the weapons into cases in the above calculations.

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You cant' equip a sentinel without a weapon, so there are 8050 + 7700 + 9800 + 354 200 + 450 800 + 431 200 + 19 835 200 = 21 096 950 impossible loadouts in your new calculations. 183 844 850 - 21 096 950 = 162 747 900.

And splitting loadouts into cases isn't necessary, it's even easier to calculate without doing it.

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You cant' equip a sentinel without a weapon, so there are 8050 + 7700 + 9800 + 354 200 + 450 800 + 431 200 + 19 835 200 = 21 096 950 impossible loadouts in your new calculations. 183 844 850 - 21 096 950 = 162 747 900.

And splitting loadouts into cases isn't necessary, it's even easier to calculate without doing it.

You can, if I remember correctly.

EDIT: Just checked, you cannot. But besides, your calculations assume that the player chooses only the new MK-1 weapons (MK-1 Braton, Lato, Skana). If not, then it would be:

nCr(25, 1) * nCr(53, 1) * ((46*44*56) - 1) = 150,179,475

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