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Combinations Permutations ની ગણતરી કેવી રીતે કરવી

Combinations Permutations શું છે?

Combinations count ways to choose items where order does not matter. Permutations count ways where order does matter. Both use factorials and appear in probability, statistics, and combinatorics.

પગલું દ્વારા પગલું માર્ગદર્શિકા

  1. 1Permutations (order matters): P(n,r) = n! / (n−r)!
  2. 2Combinations (order irrelevant): C(n,r) = n! / (r!(n−r)!)
  3. 3Rule of thumb: if you can swap two items and get a different result, use permutations

Worked Examples

ઇનપુટ
Choose 3 from 10 (order matters)
પરિણામ
720
P(10,3) = 10×9×8 = 720
ઇનપુટ
Choose 3 from 10 (order irrelevant)
પરિણામ
120
C(10,3) = 720/6 = 120
ઇનપુટ
Lotto: 6 from 49
પરિણામ
13,983,816
C(49,6)

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