Counting principles

इस पर आधारित

5 अनिवार्य पूर्वापेक्षाएँ (बिल्कुल नीचे तक)

आप सीखेंगे

• Apply the addition and multiplication principles to count outcomes.
• Count arrangements of n objects (n!) and ordered selections of k objects from n.
• Use complementary counting, for example to count passwords containing at least one digit.

परिभाषा

• n! = n × (n − 1) × ⋯ × 1 for n ≥ 1, and 0! = 1.
• A permutation is an ordered arrangement of objects.

प्रमेय

• Addition principle: if A and B are disjoint finite sets, |A ∪ B| = |A| + |B|.
• Multiplication principle: |A × B| = |A| · |B|.
• The number of ordered selections of k objects from n distinct objects is n!/(n − k)!.

आम भ्रांतियाँ

• Adding where the multiplication principle applies, or multiplying where the addition principle applies.
• Counting overlapping cases twice.

आगे ले जाता है

वैकल्पिक खोजें

• Probability Counting equally likely outcomes gives probabilities.